Maharashtra State BoardHSC Arts 11th
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Prove the following: tan2θ − sin2θ = sin4θ sec2θ - Mathematics and Statistics

Sum

Prove the following:

tan2θ − sin2θ = sin4θ sec2θ

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Solution

L.H.S. = tan2θ − sin2θ

= `sin^2theta/cos^2theta - sin^2theta`

= `sin^2theta (1/cos^2theta - 1)`

= `(sin^2theta(1 - cos^2theta))/cos^2theta`

= (sin2θ) (sin2θ) sec2θ

= sin4θ sec2θ

= R.H.S.

Concept: Fundamental Identities
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 2 Trigonometry - 1
Miscellaneous Exercise 2 | Q 10. (x) | Page 34
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