Solution of Chapter 6. Trigonometric Identities (RD Sharma - Mathematics Book)

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

If prove that

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

Prove the following trigonometric identities:

If and prove that

and , prove that .

If , , prove that .

If , , prove that

.

If , prove that .

If , prove that .

If and , prove that

If and , prove that .

If , prove that

Prove that:

(i)

(ii)

(iii)

(iv)

If , prove that

Given that:

Show that one of the values of each member of this equality is sin sinsin

If prove that

If , and , show that

If , find all other trigonometric ratios of angle .

If , find all other trigonometric ratios of angle

If , find the value of

If , find the value of

If , find the value of

If , find the value of

If , find the value of

If , find the value of

If , find the value of

If , find the value of

If , find the value of

If, find .

Define an identity.

What is the value of (1 – cos²θ) cosec²θ?

What is the value of (1 + cot²θ) sin²θ?

What is the value of ?

If sec θ + tanθ = x, write the value of sec θ − tan θ in terms of x.

If cosec θ − cot θ = α, write the value of cosec θ + cot α.

Write the value of cosec² (90° − θ) − tan²θ.

Write the value of sin A cos (90° − A) + cos A sin (90° − A).

Write the value of .

If x = a sin θ and y = b cos θ, what is the value of b²x² + a²y² ?

If , what is the value of cot θ + cosec θ?

What is the value of 9 cot²θ − 9 cosec²θ?

What is the value of ?

What is the value of ?

What is the value of (1 + tan²θ) (1 − sin θ) (1 + sin θ)?

If , find the value of tan A + cot A.

If , then find the value of 2 cot²θ + 2.

If , then find the value of 9 tan²θ + 9.

If sec²θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.

If cosec²θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.

If sin²θ cos²θ (1 + tan²θ) (1 + cot²θ) = λ, then find the value of λ.

If 5x = sec θ and , find the value of .

If cosec θ = 2x and , find the value of

If sec θ + tan θ = x, then sec θ =

If sec θ + tan θ = x, then tan θ =

is equal to

The value of is

sec⁴ A − sec² A is equal to

cos⁴ A − sin⁴ A is equal to

is equal to

is equal to

The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is

is equal to

(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal

If x = a cos θ and y = b sin θ, then b²x² + a²y² =

If x = a sec θ and y = b tan θ, then b²x²− a²y² =

is equal to

2(sin⁶θ + cos⁶θ) − 3(sin⁴θ + cos⁴θ) is equal to

If a cos θ + b sin θ and a sin θ − b cos θ = 3, then a² + b² =

If a cot θ + b cosec θ = p and b cot θ + a cosec θ = q, then p²− q² =

The value of sin² 29° + sin² 61° is

If x = r sin θ cos φ, y = r sin θ sin φ and z = r cos θ, then

If sin θ + sin² = 1, then cos²θ + cos⁴θ =

If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a² + b² =

If cos A + cos² A = 1, then sin² A + sin⁴ A

If x = a sec θ cos φ, y = b sec θ sin φ and z = c tan θ, then

If a cos θ − b sin θ = c, then a sin θ + b cos θ =

9 sec² A − 9 tan² A is equal to

(1 + tan θ + sec θ) (1 + cot θ − cosec θ) =

(sec A + tan A) (1 − sin A) =

is equal to