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प्रश्न
Prove that `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2 = sin A.cos A`
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उत्तर
LHS = `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2`
= `tan A/(sec^2 A)^2 + cot A/(cosec^2 A)^2`
= `sin A/cos A xx cos^2 A xx cos^2 A + cos A/sin A xx sin^2 A xx sin^2 A`
= sin A.cos3A + sin3A.cos A
= sin A cos A (cos2 A + sin2 A)
= sin A. cos A x 1
= sin A. cos A
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities.
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`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S = `square`
= `cos^2theta xx square .....[1 + tan^2theta = square]`
= `(cos theta xx square)^2`
= 12
= 1
= R.H.S
