Advertisements
Advertisements
Question
if `sin theta = 3/4` prove that `sqrt(cosec^2 theta - cot)/(sec^2 theta - 1) = sqrt7/3`
Advertisements
Solution
We have `sin theta = 3/4`
In ΔABC
`AC^2 = AB^2 + BC^2`
`=> (4)^2 = (3)^2 + BC^2`
`=> BC^2= 16 - 9`
`=> BC^2 = 7`
`=> BC = sqrt7`
`:. cosec theta = 4/3, sec theta = 4/sqrt7 and cot theta = sqrt7/3`
Now
L.H.S `sqrt((cosec^2 theta - cot^2 theta)/(sec^2 theta - 1))`
`= sqrt(((4/3)^2 - (sqrt7/3)^2)/((4/sqrt7)^2 - 1)`
`= sqrt((16/9 - 7/9)/(16/7 - 1)`
`=sqrt((9/9)/((16 - 7)/7 ))`
`= sqrt(7/9)`
`= sqrt7/3`
= R.H.S
APPEARS IN
RELATED QUESTIONS
If sin A = `3/4`, calculate cos A and tan A.
Given sec θ = `13/12`, calculate all other trigonometric ratios.
In ΔABC, right angled at B. If tan A = `1/sqrt3` , find the value of
- sin A cos C + cos A sin C
- cos A cos C − sin A sin C
If 3 cot θ = 2, find the value of `(4sin theta - 3 cos theta)/(2 sin theta + 6cos theta)`.
If tan θ = `a/b` prove that `(a sin theta - b cos theta)/(a sin theta + b cos theta) = (a^2 - b^2)/(a^2 + b^2)`
Evaluate the following
sin2 30° + sin2 45° + sin2 60° + sin2 90°
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
Evaluate the Following
`(sin 30^@ - sin 90^2 + 2 cos 0^@)/(tan 30^@ tan 60^@)`
If sin (A − B) = sin A cos B − cos A sin B and cos (A − B) = cos A cos B + sin A sin B, find the values of sin 15° and cos 15°.
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
If cosec θ - cot θ = `1/3`, the value of (cosec θ + cot θ) is ______.
If sin 2A = `1/2` tan² 45° where A is an acute angle, then the value of A is ______.
Find the value of sin 0° + cos 0° + tan 0° + sec 0°.
Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`
If `θ∈[(5π)/2, 3π]` and 2cosθ + sinθ = 1, then the value of 7cosθ + 6sinθ is ______.
If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2.
Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.
In ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.
