Advertisements
Advertisements
प्रश्न
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
Advertisements
उत्तर
L.H.S = `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2`
= `(1 + sin^2theta + cos^2theta + 2sintheta - 2sintheta cos theta - 2costheta)/(1 + sin^2theta + cos^2theta + 2sintheta + 2sintheta costheta + 2costheta)`
= `(1 + 1 + 2sintheta (1 - cos theta) - 2cos theta)/(1 + 1 + 2sin theta + 2cos theta (sin theta + 1))`
= `(2(1 - cos theta) + 2sintheta (1 - cos theta))/(2(1 + sin theta) + 2cos theta(1 + sin theta))`
= `(2(1 - costheta)(1 + sintheta))/(2(1 + sintheta)(1 + costheta))`
= `((1 - cos theta))/((1 + cos theta))`
L.H.S = R.H.S
Hence it is proved.
APPEARS IN
संबंधित प्रश्न
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
Without using trigonometric tables evaluate
`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80^@)`
Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =
2 (sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) is equal to
If cos (\[\alpha + \beta\]= 0 , then sin \[\left( \alpha - \beta \right)\] can be reduced to
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
