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# If $$sec 4 A \ = \ cosec (A – 20°)$$ , where 4 A is an acute angle, find the value of A.

Answer :

Given, $$sec 4A \ = \ cosec (A – 20°)$$
We know that, $$cosec(90° - \theta ) \ = \ sec\theta$$

=> $$cosec (90°– 4A) \ = \ sec 4A$$

∴ $$cosec (90° – 4A) \ = \ cosec (A – 20°)$$

=> $$90° – 4A \ = \ A – 20°$$ [$$\because$$ (90° – 4A) and (A – 20°) are both acute angles]

$$4A + A \ = \ 20° + 90°$$

=> $$5A \ = \ 110°$$

=> $$A \ = \ 22°$$