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рдкреНрд░рд╢реНрди
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
рдЙрддреНрддрд░
ЁЭР┐ЁЭР╗ЁЭСЖ = `(tan theta)/(1+tan^2 theta )^2 +( cot theta )/(1+cot^2 theta)^2`
=`tan theta/ ((sec^2 theta)^2) + cot theta/((cosec^2 theta) ^2)`
=`tan theta / sec^4 theta + cottheta/(cosec^4 theta)`
=`sin theta/cos theta xx cos^4 theta + cos theta/sin theta xx sin ^4 theta`
=` sin theta cos ^3 theta + cos theta sin ^3 theta`
=`sin theta cos theta ( cos^2 theta + sin ^2 theta)`
=`sin theta cos theta`
= RHS
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Prove that:
sec2θ + cosec2θ = sec2θ x cosec2θ
If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p
Prove the following trigonometric identities
cosec6θ = cot6θ + 3 cot2θ cosec2θ + 1
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
if `cosec theta - sin theta = a^3`, `sec theta - cos theta = b^3` prove that `a^2 b^2 (a^2 + b^2) = 1`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Prove the following identities:
`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2 =
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
For ΔABC , prove that :
`tan ((B + C)/2) = cot "A/2`
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = cosec θ - cot θ`.
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`
