Question

evaluate:-

sin²23° + sin² 67°​

Answer 1

Answer:

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Given→

sin²1° + sin²23° + sin² 45 ° + sin² 67° + sin² 89°

Because there is a difference of 22° among all terms .

Solution→

Sin²1 ° can be written in the form of cos theta as

sin theta = cos (90- theta )

sin ²1. = cos² ( 90-1 )

Sin²1°. = cos²89°

Similarly →

sin²23°. = cos²( 90- 23)

sin²23°. = cos²67°

Now putting theses values in given series.

(cos²89° + sin²89°) +(cos²67° +sin²67°) +sin²45°

we know that sin²a + cos²a = 1 and value of sin 45° = 1/√2

→ 1 + 1 +( 1/√2 )²

→ 2 + 1/2

→ 5 /2

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Answer 2

Answer: 1

Step-by-step explanation: 90 - 67 = 23

sin^2(90-67) = cos^2 (23)

so, sin^2 (23) + cos^2 (23) = 1

as sin^2 (Theta) + cos^2(theta) = 1