Advertisements
Advertisements
प्रश्न
Prove the following identities:
`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`
Advertisements
उत्तर
L.H.S. = tan A – cot A
= `(sin A)/(cos A) - (cos A)/(sin A)`
= `(sin^2A - cos^2A)/(sin A cos A)`
= `(1 - cos^2A - cos^2A)/(sin A cos A)` ...(∵ sin2A = 1 – cos2A)
= `(1 - 2cos^2A)/(sin A cos A)`
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`
if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2 = 2`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =
Prove the following identity :
`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`
Prove that tan2Φ + cot2Φ + 2 = sec2Φ.cosec2Φ.
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot θ)`
If 2sin2θ – cos2θ = 2, then find the value of θ.
