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рдкреНрд░рд╢реНрди
`(1+ cos theta - sin^2 theta )/(sin theta (1+ cos theta))= cot theta`
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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.
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
cosec4θ − cosec2θ = cot4θ + cot2θ
`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
Show that none of the following is an identity:
`tan^2 theta + sin theta = cos^2 theta`
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
What is the value of \[\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}\]
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
If cos A + cos2 A = 1, then sin2 A + sin4 A =
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Find x , if `cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`
Prove that `((1 + sin θ - cos θ)/( 1 + sin θ + cos θ))^2 = (1 - cos θ)/(1 + cos θ)`.
Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.
If 2sin2θ – cos2θ = 2, then find the value of θ.
Show that, cotθ + tanθ = cosecθ × secθ
Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
