Question

if sin square A = 1/2 tan square 45° where A is an acute angle then find the value of A

Answer 1

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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Answer 2

Answer:

A = 45°

Step-by-step explanation:

Given:- sin² A = 1/2 tan² 45° where A is an acute angle.

To find:- The value of A .

Solution:-

An acute angle is an angle whose value measures less than 90°. For Example - 30°, 45°, 65°, etc.

So, A will be less than 90°.

The given expression is

sin² A = 1/2 tan² 45°

⇒ sin² A = $\frac{1}{2}$ × ( 1 )²            [∵ Acc. to trigonometric formulas, tan 45° = 1]

⇒ sin² A =  $\frac{1}{2}$

⇒ sin A = √$\frac{1}{2}$

⇒ sin A = $\frac{1}{\sqrt{2} }$

⇒ A = 45°        [∵ sin 45° = 1/√2]

Therefore, the value of A is 45°.

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