Advertisements
Advertisements
प्रश्न
`(1+ cos theta + sin theta)/( 1+ cos theta - sin theta )= (1+ sin theta )/(cos theta)`
उत्तर
LHS =` (1+ cos theta + sin theta)/(1+ cos theta-sin theta)`
=` ({(1+cos theta)+ sin theta}{(1+ cos theta)+ sin theta})/({(1+ cos theta )-sin theta}{(1+ cos theta )+ sin theta}) {"Multiplying the numerator and denominator by "(1 + costheta +sin theta}`
=`({(1+ cos theta)+ sin theta}^2)/({(1+ cos theta )^2-sin ^2 theta})`
=`(1+ cos^2 theta + 2 cos theta + sin ^2 theta + 2 sin theta (1+ cos theta))/(1+ cos^2 theta + 2 cos theta - sin ^2 theta)`
=`(2+2 cos theta + 2 sin theta (1+ cos theta))/(1+ cos ^2 theta + 2 cos theta -(1-cos^2 theta))`
=`(2(1+ cos theta)+2sin theta (1+ cos theta))/(2 cos^2 theta+2 cos theta)`
=`(2(1+ cos theta) (1+ sin theta))/( 2 cos theta (1+ cos theta))`
=`(1+sin theta)/cos theta`
= RHS
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`
`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`
`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`
`(1+tan^2A)/(1+cot^2A)` = ______.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
Prove the following trigonometric identities
(1 + cot2 A) sin2 A = 1
Prove the following trigonometric identities
tan2 A + cot2 A = sec2 A cosec2 A − 2
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
Prove the following identity :
`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`
Prove the following identity :
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Find the value of sin 30° + cos 60°.
There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ, then prove that x2 + y2 = 1
Choose the correct alternative:
sec 60° = ?
Prove that
sec2A – cosec2A = `(2sin^2"A" - 1)/(sin^2"A"*cos^2"A")`
If 2sin2θ – cos2θ = 2, then find the value of θ.
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
