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рдкреНрд░рд╢реНрди
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
рдЙрддреНрддрд░
LHS = `(1- tan^2 theta)/(cot^2 theta-1)`
=`(1-(sin^2 theta)/(cos^2 theta))/((cos^2 theta )/(sin^2 theta)-1)`
=`((cos^2 theta - sin^2 theta)/(cos^2 theta))/((cos^2theta-sin^2 theta)/(sin^2 theta))`
=`(sin^2 theta)/(cos^2 theta)`
= tan2 ЁЭЬГ
= RHS
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рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
Prove the following trigonometric identities.
`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta)/cos theta`
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
If `secθ = 25/7 ` then find tanθ.
What is the value of \[\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}\]
If sin θ − cos θ = 0 then the value of sin4θ + cos4θ
Prove the following identity :
`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Prove that `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`
Find the value of ( sin2 33° + sin2 57°).
Prove that `( 1 + sin θ)/(1 - sin θ) = 1 + 2 tan θ/cos θ + 2 tan^2 θ` .
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
Choose the correct alternative:
cos θ. sec θ = ?
Prove that `(sintheta + tantheta)/cos theta` = tan θ(1 + sec θ)
