Advertisements
Advertisements
प्रश्न
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
Advertisements
उत्तर
LHS = `((sin^2 A + ( 1 + cos A)^2)/((1 + cos A)sin A))`
= `(sin^2 A + 1 + cos^2 A + 2 cos A)/((1 + cos A) sin A)`
= `(1 + 1 + 2 cos A)/((1 + cos A) sin A)`
= `(2(1 + cos A))/((1 + cos A)sin A)`
= 2 cosec A
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities.
`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`
Prove the following identities:
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`
Prove that `( sintheta - 2 sin ^3 theta ) = ( 2 cos ^3 theta - cos theta) tan theta`
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
Prove that : `tan"A"/(1 - cot"A") + cot"A"/(1 - tan"A") = sec"A".cosec"A" + 1`.
`sin θ = 1/2`, then θ = ?
If `1 - cos^2θ = 1/4`, then θ = ?
Prove that `(cot A)/(1 - tan A) + (tan A)/(1 - cot A) = 1 + tan A + cot A = sec A . "cosec" A + 1`.
