Write the least value of cos2 x + sec2 x.

We know that cos2x and sec2x ≥ 0∴ By applying AM and GM we get,⇒ ⇒ cos2 x + sec2 x≥2∴ Least value of the given function is 2.

Q15 of 118 Page 5

Write the least value of cos² x + sec² x.

We know that cos²x and sec²x ≥ 0

∴ By applying AM and GM we get,

⇒

⇒ cos² x + sec² x≥2

∴ Least value of the given function is 2.

If cot (α + β) = 0, then write the value of sin (α + 2β).

If tan A + cot A = 4, then write the value of tan⁴ A + cot⁴ A.

If x = sin¹⁴x + cos²⁰ x, then write the smallest interval in which the value of x lie.

If 3 sin x + 5 cos x = 5, then write the value of 5 sin x − 3 cos x.