Question

The value of sin² 5+ sin²10+sin²15________ +sin²85 + sin²90is equal to

Answer 1

Tᴏ Fɪɴᴅ :-

value of sin² 5+ sin²10+sin²15________ +sin²85 + sin²90 ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• sin(90 - A) = cosA
• sin²A + cos²A = 1 .
• sin45° = (1/√2)
• sin90° = 1

Sᴏʟᴜᴛɪᴏɴ :-

→ sin85 can be written as = sin(90 - 5) = cos5

Similarly,

→ sin80 = sin(90 - 10) = cos10

→ sin75 = sin(90 - 15) = cos15

_____________

_____________

_____________

→ sin50 = sin(90 - 40) = cos40° .

= Total Terms = 40/5 = 8 Terms.

___________

Now, After Putting These values Our Question becomes :-

➪ sin² 5+ sin²10+sin²15_________+cos²15 + cos²10 +cos²85 + sin²90

➪ (sin²5 + cos²5) + (sin²10 + cos²10) + (sin²15 + cos²15) ______________ + (sin²40 + cos²40) + sin²45 + sin²90

➪ 1 + 1 + 1 __________ 1 + (1/√2)² + (1)²

➪ 8 + (1/2) + 1

➪ 9 + (1/2)

➪ 9(1/2) (Ans.)

Answer 2

Answer:

Please find attachment

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