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рдкреНрд░рд╢реНрди
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
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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
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Prove the following trigonometric identities.
tan2 θ − sin2 θ = tan2 θ sin2 θ
Prove the following trigonometric identities:
sin2 A cot2 A + cos2 A tan2 A = 1
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
Show that none of the following is an identity:
`sin^2 theta + sin theta = 2`
If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`
Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\]
If \[\cos \theta = \frac{3}{4}\] then find the value of 9 tan2 θ + 9.
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
If cosθ = `5/13`, then find sinθ.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `± sqrt(a^2 + b^2 - c^2)`
Prove the following:
`1 + (cot^2 alpha)/(1 + "cosec" alpha)` = cosec α
