If 0 < θ < 90 and secθ = cosec60, find the value of 2cos2θ — 1.

secθ = cosec60⇒ secθ =⇒ θ = 30Now,2cos2— 1= 2cos230— 1

Q10 of 104 Page 196

If 0 < θ < 90 and secθ = cosec60, find the value of 2cos²θ — 1.

secθ = cosec60

⇒ secθ =

⇒ θ = 30

Now,

2cos²— 1

= 2cos²30— 1

If tanA = cotB, prove that A + B = 90, where A and B are measures of acute angles.

If sec2A = cosec(A — 42), where 2A is the measure of an acute angle, find the value of A.

Prove the following by using trigonometric identities:

2sin²θ + 4sec²θ + 5cot²θ + 2cos²θ — 4tan²θ — 5cosec²θ = 1