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प्रश्न
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
उत्तर
LHS = cosecA + cotA
= `(cosecA + cotA)/1 . (cosecA - cotA)/(cosecA - cotA)`
= `(cosec^2A - cot^2A)/(cosecA - cotA) = (1 + cot^2A - cot^2A)/(cosecA - cotA)`
= `1/(cosecA - cotA)`
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संबंधित प्रश्न
Prove the following identities:
`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
`1/((1+ sintheta ))+1/((1- sin theta ))= 2 sec^2 theta`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
Prove the following identity :
`(1 + sinA)/(1 - sinA) = (cosecA + 1)/(cosecA - 1)`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Prove that `( 1 + sin θ)/(1 - sin θ) = 1 + 2 tan θ/cos θ + 2 tan^2 θ` .
`5/(sin^2theta) - 5cot^2theta`, complete the activity given below.
Activity:
`5/(sin^2theta) - 5cot^2theta`
= `square (1/(sin^2theta) - cot^2theta)`
= `5(square - cot^2theta) ......[1/(sin^2theta) = square]`
= 5(1)
= `square`
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
