Advertisements
Advertisements
प्रश्न
Prove the following identity :
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Advertisements
उत्तर
LHS = `1/(sinA + cosA) + 1/(sinA - cosA)`
= `(sinA - cosA + sinA + cosA)/(sin^2A - cos^2A)`
= `(2sinA)/(1 - cos^2A - cos^2A) = (2sinA)/(1 - 2cos^2A)`
APPEARS IN
संबंधित प्रश्न
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
Prove the following trigonometric identities.
`(sec A - tan A)/(sec A + tan A) = (cos^2 A)/(1 + sin A)^2`
Prove the following trigonometric identities.
`((1 + sin theta - cos theta)/(1 + sin theta + cos theta))^2 = (1 - cos theta)/(1 + cos theta)`
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
Prove the following identities:
sec2A + cosec2A = sec2A . cosec2A
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ, then prove that x2 + y2 = 1
sin2θ + sin2(90 – θ) = ?
Prove that `(sin θ + tan θ)/(cos θ) = tan θ (1 + sec θ)`.
