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प्रश्न
`(1-cos^2theta) sec^2 theta = tan^2 theta`
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उत्तर
LHS = `(1-cos^2 theta)sec^2 theta`
=`sin^2 theta xx sec^2 theta (∵ sin^2 theta + cos^2 theta = 1)`
= `sin^2 theta xx 1/(cos^2 theta)`
=`(sin^2 theta)/(cos^2 theta)`
=`tan^2 theta`
=RHS
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संबंधित प्रश्न
`(1+tan^2A)/(1+cot^2A)` = ______.
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
`(cos theta cosec theta - sin theta sec theta )/(costheta + sin theta) = cosec theta - sec theta`
If`( 2 sin theta + 3 cos theta) =2 , " prove that " (3 sin theta - 2 cos theta) = +- 3.`
If m = ` ( cos theta - sin theta ) and n = ( cos theta + sin theta ) "then show that" sqrt(m/n) + sqrt(n/m) = 2/sqrt(1-tan^2 theta)`.
Define an identity.
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
Prove that cosec θ – cot θ = `(sin θ)/(1 + cos θ)`.
Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)
Show that tan4θ + tan2θ = sec4θ – sec2θ.
