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`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
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LHS = `(1- tan^2 theta)/(cot^2 theta-1)`
=`(1-(sin^2 theta)/(cos^2 theta))/((cos^2 theta )/(sin^2 theta)-1)`
=`((cos^2 theta - sin^2 theta)/(cos^2 theta))/((cos^2theta-sin^2 theta)/(sin^2 theta))`
=`(sin^2 theta)/(cos^2 theta)`
= tan2 ЁЭЬГ
= RHS
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Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
Prove the following trigonometric identities.
`tan A/(1 + tan^2 A)^2 + cot A/((1 + cot^2 A)) = sin A cos A`
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
If tan A = n tan B and sin A = m sin B, prove that:
`cos^2A = (m^2 - 1)/(n^2 - 1)`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
Prove that:
`"tanθ"/("secθ" – 1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`
If x = a sec θ cos ╧Х, y = b sec θ sin ╧Х and z = c tan θ, then\[\frac{x^2}{a^2} + \frac{y^2}{b^2}\]
If sin θ = `1/2`, then find the value of θ.
If cosθ = `5/13`, then find sinθ.
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
If 1 – cos2θ = `1/4`, then θ = ?
Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.
