Question

express sin 75 degrees+ cos 65 degrees in terms of trigonometric ratios of angles between 0 degrees and 45 degrees.
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Answer 1

Aɴsᴡᴇʀ :-

• cos 15 + sin 25

Qᴜᴇsᴛɪᴏɴ :-

express sin 75 degrees+ cos 65 degrees in terms of trigonometric ratios of angles between 0 degrees and 45 degrees.

Cᴏɴᴄᴇᴘᴛ :-

• sin(90 - Θ ) = cosΘ
• cos (90 - Θ) = sinΘ

Sᴏʟᴜᴛɪᴏɴ :-

➪sin 75 + cos 65

= cos ( 90 - 75) + sin ( 90 - 65)

= cos 15 + sin 25

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Answer 2

Answer:-

Your Answer Is Cos 15° + Sin 25°.

Explanation:-

Given trigonometric ratios:-

• Sin 75° + Cos 65°.

To Express:-

• The given ratios of angles between 0 - 45 degrees.

Concept Used:-

• ↦ Sinθ = Cos(90° - θ).

• ↦ Cosθ = Sin(90° - θ).

Now,

↦ Sin 75° + Cos 65°.

= Cos(90° - 75°) + Sin(90° - 65°).

= Cos 15° + Sin 25°.

Also the above angles are between 0 - 45 degrees so this is our required answer.

More Trigonometric IDs:-

• ↦ Sin²θ + Cos²θ = 1.

• ↦ 1 + tan²θ = Cosec²θ.

• ↦ 1 + Cot²θ = Cosec²θ.