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प्रश्न
`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`
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उत्तर
`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`
LHS=`cos^2theta/((1-tan theta))+sin ^3theta/((sin theta - cos theta))`
=`cos^2theta/(1-sintheta/costheta)+sin^3 theta/((sin theta-costheta))`
=`cos^3 theta/((cos theta-sin theta))+ sin ^3 theta/((sintheta-cos theta))`
=`(cos^3theta-sin^3 theta)/((costheta - sin theta))`
=`((cos theta-sintheta)(cos^2 theta+cos theta sin +sin^2theta))/((costheta-sintheta))`
=`(sin^2theta + cos^2 theta + cos theta sin theta)`
=`(1+sin theta cos theta)`
=RHS
Hence, L.H.S = R.H.S.
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संबंधित प्रश्न
Prove the following trigonometric identities.
`cosec theta sqrt(1 - cos^2 theta) = 1`
Prove the following trigonometric identities
`(1 + tan^2 theta)/(1 + cot^2 theta) = ((1 - tan theta)/(1 - cot theta))^2 = tan^2 theta`
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x2 + y2 + z2 = r2
Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`
Prove the following identities:
`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
`(sec^2 theta-1) cot ^2 theta=1`
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
Write the value of cosec2 (90° − θ) − tan2 θ.
Prove the following identity :
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
Evaluate:
`(tan 65°)/(cot 25°)`
Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
Prove that `1/("cosec" theta - cot theta)` = cosec θ + cot θ
Prove that `sec"A"/(tan "A" + cot "A")` = sin A
