Advertisements
Advertisements
प्रश्न
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
उत्तर
LHS = secA(1 + sinA)(secA - tanA)
= `1/cosA(1 + sinA)(1/cosA - sinA/cosA)`
= `((1 + sinA))/cosA((1-sinA)/cosA) = (1-sin^2A)/cos^2A`
= `(cos^2A/cos^2A) = 1` = RHS
APPEARS IN
संबंधित प्रश्न
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Prove the following trigonometric identities.
sin2 A cot2 A + cos2 A tan2 A = 1
Prove the following trigonometric identities.
`(1 + sin theta)/cos theta + cos theta/(1 + sin theta) = 2 sec theta`
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities.
`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A`
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`
If a cos `theta + b sin theta = m and a sin theta - b cos theta = n , "prove that "( m^2 + n^2 ) = ( a^2 + b^2 )`
Write the value of tan10° tan 20° tan 70° tan 80° .
Prove that `"cot A"/(1 - cot"A") + "tan A"/(1 - tan "A")` = – 1
