Advertisements
Advertisements
प्रश्न
Prove the following identities:
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Advertisements
उत्तर
L.H.S. = `1/(sinA + cosA) + 1/(sinA - cosA)`
= `(sinA - cosA + sinA + cosA)/((sinA + cosA)(sinA - cosA))`
= `(2sinA)/(sin^2A - cos^2A)`
= `(2sinA)/(1 - cos^2A - cos^2A)` ...(∵ sin2A = 1 – cos2A)
= `(2sinA)/(1 - 2cos^2A)`
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
`sqrt((1 + sin θ)/(1 - sin θ)) = sec θ + tan θ`
If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.
Prove that `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Prove that `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.
(sec θ + tan θ) . (sec θ – tan θ) = ?
Show that tan4θ + tan2θ = sec4θ – sec2θ.
