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प्रश्न
Prove that :(sinθ+cosecθ)2+(cosθ+ secθ)2 = 7 + tan2 θ+cot2 θ.
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उत्तर
L.H.S : (sinθ+cosecθ)2 +(cosθ+secθ)2
=sin2θ + cosec2θ + 2 +cos2θ + sec2θ + 2 `[because sin θ = 1/(cosecθ) " and cos "θ = 1/ (secθ)]`
= sin2θ + cos2θ+1+cot2θ+1+tan2θ+4 `[because cosec^2θ+1+cot^2θ" and "sec^2 θ =1+ tan^2θ]`
=sin2θ+cos2θ+1+cot2θ+1+tan2θ+4 `[because cosec^2θ+1+cot^2θ " and" sec^2 θ=1 +tan^2θ]`
=1+1+1+4+tan2θ+cot2θ `[because cos^2θ+ sin^2θ=1]`
=7+ tan2θ+cot2θ
L.H.S-R.H.S
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संबंधित प्रश्न
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
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`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
Define an identity.
What is the value of (1 + cot2 θ) sin2 θ?
Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\]
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
