Advertisements
Advertisements
प्रश्न
Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
Advertisements
उत्तर
L.H.S. = cosec4 A – cosec2 A
= cosec2 A (cosec2 A – 1)
R.H.S. = cot4 A + cot2 A
= cot2 A (cot2 A + 1)
= (cosec2 A – 1) cosec2 A
Thus, L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
Evaluate sin25° cos65° + cos25° sin65°
The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.
`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
Prove that `(cot A)/(1 - cot A) + (tan A)/(1 - tan A) = -1`.
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
