If A+B=90^o, then fill up the blanks with suitable trigonometric ratio of complementary angle of A or B.

(i) sin A =…. (ii) cos B =…

(iii) sec A =… (iv) tan B =…

(v) cosec B =… (vi) cot A=…

(i) Here, A+B = 90°

⇒ A = 90° - B

Multiplying both sides by Sin, we get

Sin A = Sin (90° - B)

⇒ sin A = Cos B [∵ cos θ = sin (90° - θ)]

(ii) Here, A+B = 90°

⇒ B = 90° - A

Multiplying both sides by cos, we get

Cos B = cos (90° - A)

⇒ cos B = sin A [∵ Sin θ = cos (90° - θ)]

(iii) Here, A+B = 90°

⇒ A = 90° - B

Multiplying both sides by sec, we get

Sec A = Sec (90° - B)

⇒ sec A = Cosec B [∵ cosec θ = sec (90° - θ)]

(iv) Here, A+B = 90°

⇒ B = 90° - A

Multiplying both sides by tan, we get

tan B = tan (90° - A)

⇒ tan B = cot A [∵ cot θ = tan (90° - θ)]

(v) Here, A+B = 90°

⇒ B = 90° - A

Multiplying both sides by cosec, we get

Cosec B = cosec (90° - A)

⇒ cosec B = sec A [∵ sec θ = cosec (90° - θ)]

(vi) Here, A+B = 90°

⇒ A = 90° - B

Multiplying both sides by Sin, we get

cotA = cot (90° - B)

⇒ cot A = tan B [∵ tan θ = cot (90° - θ)]