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рдкреНрд░рд╢реНрди
`(1+ cos theta - sin^2 theta )/(sin theta (1+ cos theta))= cot theta`
рдЙрддреНрддрд░
LHS= `(1+ cos theta - sin^2 theta )/(sin theta (1+ cos theta)`
=` ((1+ cos theta )- (1-cos^2 theta))/(sin theta(1+ cos theta))`
=`(cos theta + cos^2 theta)/( sin theta ( 1+ cos theta))`
=`(cos theta ( 1+ cos theta ))/ ( sin theta ( 1+ cos theta))`
=`cos theta/ sin theta`
= cot ЁЭЬГ
= RHS
Hence, L.H.S. = R.H.S.
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рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
Prove that:
sec2θ + cosec2θ = sec2θ x cosec2θ
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Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
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(i) `cos^2theta + cos theta =1`
Prove that `( sintheta - 2 sin ^3 theta ) = ( 2 cos ^3 theta - cos theta) tan theta`
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If \[\sin \theta = \frac{1}{3}\] then find the value of 9tan2 θ + 9.
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 :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Prove that `((1 + sin θ - cos θ)/( 1 + sin θ + cos θ))^2 = (1 - cos θ)/(1 + cos θ)`.
Choose the correct alternative:
sec 60° = ?
Prove that `(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ
(sec2 θ – 1) (cosec2 θ – 1) is equal to ______.
