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Prove the following: sin4θ +2sin2θ . cos2θ = 1 − cos4θ

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Question

Prove the following:

sin⁴θ +2sin²θ . cos²θ = 1 − cos⁴θ

Sum

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Solution

L.H.S. =sin⁴θ +2sin²θ . cos²θ

= sin²θ(sin²θ + 2cos²θ)

= (sin²θ) (sin²θ + cos²θ + cos²θ)

= (1 – cos²θ) (1 + cos²θ)

= 1 – cos⁴θ

= R.H.S.

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Important Identities and Standard Results

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Q 10) viii)Q 10) vii)Q 10) ix)

Chapter 2: Trigonometry - 1 - MISCELLANEOUS EXERCISE - 2 [Page 34]

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Balbharati Mathematics and Statistics (Arts and Science) Part 1 [English] Standard 11 Maharashtra State Board

Chapter 2 Trigonometry - 1
MISCELLANEOUS EXERCISE - 2 | Q 10) viii) | Page 34

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