Advertisements
Advertisements
प्रश्न
(sec2 θ – 1) (cosec2 θ – 1) is equal to ______.
पर्याय
–1
1
0
2
Advertisements
उत्तर
(sec2 θ – 1) (cosec2 θ – 1) is equal to 1.
Explanation:
(sec2 θ – 1) (cosec2 θ – 1) = tan2 θ.cot2 θ ...`[(∵ sec^2 θ - 1 = tan^2 θ),("cosec"^2 θ - 1 = cot^2 θ)]`
= `tan^2 θ . 1/tan^2 θ`
= 1
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 - sin θ)/(1 + sin θ) = (sec θ - tan θ)^2`
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
`(sec^2 theta-1) cot ^2 theta=1`
If `sec theta = x ,"write the value of tan" theta`.
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
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 ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
Prove that `((1 + sin θ - cos θ)/( 1 + sin θ + cos θ))^2 = (1 - cos θ)/(1 + cos θ)`.
If 3 sin θ = 4 cos θ, then sec θ = ?
Let α, β be such that π < α – β < 3π. If sin α + sin β = `-21/65` and cos α + cos β = `-27/65`, then the value of `cos (α - β)/2` is ______.
