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प्रश्न
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
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उत्तर
cosec A – cot A
= `1/sinA - cosA/sinA`
= `(1 - cosA)/sinA`
= `(1 - cosA)/sinA xx (1 + cosA)/(1 + cosA)`
= `(1 - cos^2A)/(sinA(1 + cosA)`
= `sin^2A/(sinA(1 + cosA))`
= `sinA/(1 + cosA)`
संबंधित प्रश्न
Prove the following trigonometric identities
tan2 A + cot2 A = sec2 A cosec2 A − 2
If x = a cos θ and y = b cot θ, show that:
`a^2/x^2 - b^2/y^2 = 1`
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 )`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`cos 63^circ sec(90^circ - θ) = 1`
For ΔABC , prove that :
`tan ((B + C)/2) = cot "A/2`
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
