Advertisements
Advertisements
प्रश्न
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
Prove the following:
`1 + (tan^2 θ)/(1 + sec θ) = sec θ`
Advertisements
उत्तर
LHS = `1 + (tan^2 θ)/((1 + sec θ))`
=` 1 + ((sec^2 θ - 1))/((sec theta + 1))`
=`1 + ((sec theta + 1)(sec theta - 1))/((sec theta + 1))`
=`1 + (sec theta - 1)`
= sec θ
LHS = RHS
APPEARS IN
संबंधित प्रश्न
As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
`(sin theta +cos theta )/(sin theta - cos theta)+(sin theta- cos theta)/(sin theta + cos theta) = 2/((sin^2 theta - cos ^2 theta)) = 2/((2 sin^2 theta -1))`
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
Prove that `(tan θ)/(cot(90° - θ)) + (sec (90° - θ) sin (90° - θ))/(cosθ. cosec θ) = 2`.
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
Prove that `(sin θ. cos (90° - θ) cos θ)/sin( 90° - θ) + (cos θ sin (90° - θ) sin θ)/(cos(90° - θ)) = 1`.
