Advertisements
Advertisements
प्रश्न
Prove the following identity :
`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`
Advertisements
उत्तर
LHS = `(secA - 1)/(secA + 1)`
= `(1/cosA - 1)/(1/cosA + 1) = (1 - cosA)/(1 + cosA)`
= `(1 - cosA)/(1 + cosA) xx (1 + cosA)/(1 + cosA)`
= `(1-cos^2A)/(1 + cosA)^2`
= `sin^2A/(1 + cosA)^2` (∵ `1 - cos^2A = sin^2A`)
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
sin2 A cot2 A + cos2 A tan2 A = 1
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following trigonometric identities.
if x = a cos^3 theta, y = b sin^3 theta` " prove that " `(x/a)^(2/3) + (y/b)^(2/3) = 1`
`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
