If cosec⁡2A = sec⁡(A -15^∘ ), then find the measure of A (in degrees).

Correct option is C

Given:

Cosec2A= sec (A-$$15^∘$$)

Concept used:

trigonometric identities:

cosec$$\theta$$ = $$\frac{1}{sin\theta}$$

secθ = $$\frac{1}{cos\theta}$$

Solution:

Cosec2A= sec (A-$$15^∘$$)

Rewrite using trigonometric identities:

sin2A = cos(A- $$15^∘$$)

​Using the co-function identity cos x =  sin(90- x)

​$$cos⁡(A−15^∘)=sin⁡(105^∘−A)$$

so, 

​$$sin⁡2A=sin⁡(105^∘−A)$$

​​$$2=105^∘−$$

3A = $$105^∘$$

A = 35

So, the measure of A = $$35^∘$$

Thus, correct option is (c)