Question

If sin²A=1/2tan 45°, where A is an acute angle, then find the value of A

Answer 1

Sin^2 A = 1/2 tan^2A= 1/(2*(1)^2) =1/2, As angle A is an acute angle.

So,

SinA = 1/√2 , You know value of sin 45°=1/√2

Or,

A = Sin^(-1) {1/√2} = 45°

So, A = 45°

Answer 2

Answer :

Given,

sin²A = 1/2 tan²45°

⇒ sin²A = 1/2 × 1 [∵ tan45° = 1]

⇒ sin²A = 1/2

⇒ sin²A = sin²45

⇒ sinA = sin45°,

since A is an acute angle

⇒ A = 45°

∴ A = 45°

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