Advertisements
Advertisements
प्रश्न
if `sin theta = 3/4` prove that `sqrt(cosec^2 theta - cot)/(sec^2 theta - 1) = sqrt7/3`
Advertisements
उत्तर
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
संबंधित प्रश्न
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin C, cos C
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
State whether the following are true or false. Justify your answer.
cos A is the abbreviation used for the cosecant of angle A.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
Evaluate the following
`2 sin^2 30^2 - 3 cos^2 45^2 + tan^2 60^@`
Evaluate the Following
`(sin 30^@ - sin 90^2 + 2 cos 0^@)/(tan 30^@ tan 60^@)`
Find the value of x in each of the following :
cos x = cos 60º cos 30º + sin 60º sin 30º
Find the value of x in the following :
cos 2x = cos 60° cos 30° + sin 60° sin 30°
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°.
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
If cos A + cos² A = 1, then sin² A + sin4 A is equal to ______.
If sin θ + sin² θ = 1, then cos² θ + cos4 θ = ______.
Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`
Let f(x) = sinx.cos3x and g(x) = cosx.sin3x, then the value of `7((f(π/7) + g(π/7))/(g((5π)/14) + f((5π)/14)))` is ______.
If f(x) = `3cos(x + (5π)/6) - 5sinx + 2`, then maximum value of f(x) is ______.
If sinθ = `1/sqrt(2)` and `π/2 < θ < π`. Then the value of `(sinθ + cosθ)/tanθ` is ______.
If θ is an acute angle of a right angled triangle, then which of the following equation is not true?
