Advertisements
Advertisements
प्रश्न
`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`
Advertisements
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.
APPEARS IN
संबंधित प्रश्न
Prove that: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
Prove that:
`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`
`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`
`(1+ cos theta - sin^2 theta )/(sin theta (1+ cos theta))= cot theta`
If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ?
If 5x = sec θ and \[\frac{5}{x} = \tan \theta\]find the value of \[5\left( x^2 - \frac{1}{x^2} \right)\]
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove the following identity :
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
If tan θ = 2, where θ is an acute angle, find the value of cos θ.
Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
Prove that cosec2 (90° - θ) + cot2 (90° - θ) = 1 + 2 tan2 θ.
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
(1 – cos2 A) is equal to ______.
