Question

sin2 29°+ sin2 69° the value
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Answer 1

Step-by-step explanation:

The value of sin2 29° + sin2 61° is

A. 1

B. 0

C. 2 sin2 29°

D. 2 cos2 61

Answer

To find: sin2 29° + sin261°

Consider sin2 29° + sin261°

∵ 29 = 90 – 61

∴ sin2 29° + sin261° = sin2 (90° – 61°) + sin2 61°

Now, as sin (90° – θ) = cos θ

⇒ sin2 29° + sin261° = sin2 (90° – 61°) + sin2 61°

= cos2 61° + sin2 61°

= 1 [sin2 θ + cos2 θ = 1]

Answer 2

Answer:

The value of sin²29° + sin²61° is 1.

Step-by-step explanation:

According to the given information, we need to find the value of

sin²29° + sin²61°.

Now, we can solve this expression and find the value of this expression by using the well-known trigonometrical property that is sin ∅ is equivalent to writing this as cos ( 90° - ∅ ).

Now, here, we can utilize this property by converting one angle into the other so that we can build up a relation between them in order to find the value ultimately.

Now, given that,

sin²29° + sin²61°.

Or,  | sin²29° | + sin²61°.

Or,  | sin 29° |² + sin²61°.

This happens because of the modulus property that is |x²| is equal to |x|².

Thus, our expression gives,

| sin 29° |² + sin²61°.

=| cos(90° -  29°) |² + sin²61°... { Since sin ∅ is equivalent to writing this as cos ( 90° - ∅ ).}

= | cos(61°) |² + sin²61°

= cos²(61°) + sin²61°

Now, by the well-known trigonometrical identity that is sin²x + cos²x = 1,

we get,

cos²(61°) + sin²61°

=1

Thus, the value of sin²29° + sin²61° is 1.

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