Advertisements
Advertisements
Question
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
Advertisements
Solution
L.H.S = `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2`
= `(1 + sin^2theta + cos^2theta + 2sintheta - 2sintheta cos theta - 2costheta)/(1 + sin^2theta + cos^2theta + 2sintheta + 2sintheta costheta + 2costheta)`
= `(1 + 1 + 2sintheta (1 - cos theta) - 2cos theta)/(1 + 1 + 2sin theta + 2cos theta (sin theta + 1))`
= `(2(1 - cos theta) + 2sintheta (1 - cos theta))/(2(1 + sin theta) + 2cos theta(1 + sin theta))`
= `(2(1 - costheta)(1 + sintheta))/(2(1 + sintheta)(1 + costheta))`
= `((1 - cos theta))/((1 + cos theta))`
L.H.S = R.H.S
Hence it is proved.
APPEARS IN
RELATED QUESTIONS
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 identities:
`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.
If `cos B = 3/5 and (A + B) =- 90° ,`find the value of sin A.
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
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.
Prove that `sec"A"/(tan "A" + cot "A")` = sin A
