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प्रश्न
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
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उत्तर
LHS = `1 - (cos^2 θ)/(1 + sin θ)`
= `1 - (1 - sin^2 θ)/(1 + sin θ)`
= `1 - ((1 - sin θ)(1 + sin θ))/(1 + sin θ)`
= 1 - ( 1 - sin θ )
= 1 - 1 + sin θ
= sin θ
= RHS
Hence proved.
संबंधित प्रश्न
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following trigonometric identities.
tan2 θ − sin2 θ = tan2 θ sin2 θ
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
`(1+tan^2theta)(1+cot^2 theta)=1/((sin^2 theta- sin^4theta))`
Write the value of `(1 + tan^2 theta ) cos^2 theta`.
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Prove that `(sec A)/(tan A + cot A) = sin A`.
