Advertisements
Advertisements
प्रश्न
Evaluate the following
`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°`
Advertisements
उत्तर
`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°` ....(i)
By trigonometric ratios we have
`sin 30^@ = 1/2` `cos 45^@ = 1/sqrt2` `tan 30^2 = 1/sqrt3` `sin 90^@ = 1 cos 90^@ = 0 cos 0^@ = 1`
By substituting above values in (i), we get
`[1/2]^2 . [1/sqrt2]^2 + 4[1/sqrt3]^2 + 1/2[1]^2 - 2[0]^2 + 1/24 [1]^2`
`1/4.1/2 + 4/ 1/3 + 1/2 - 0 + 1/24`
`1/8 + 4/3 + 1/2 + 1/24 = 48/24 = 2`
APPEARS IN
संबंधित प्रश्न
In Given Figure, find tan P – cot R.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
If `cos θ = 12/13`, show that `sin θ (1 - tan θ) = 35/156`.
if `tan theta = 12/13` Find `(2 sin theta cos theta)/(cos^2 theta - sin^2 theta)`
If `sin theta = a/b` find sec θ + tan θ in terms of a and b.
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
Evaluate the following:
(cosec2 45° sec2 30°)(sin2 30° + 4 cot2 45° − sec2 60°)
Evaluate the Following
4(sin4 30° + cos2 60°) − 3(cos2 45° − sin2 90°) − sin2 60°
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
Find the value of x in each of the following :
cos x = cos 60º cos 30º + sin 60º sin 30º
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°.
`(sin theta)/(1 + cos theta)` is ______.
If sin A = `1/2`, then the value of cot A is ______.
`sqrt(3)` cos2A + `sqrt(3)` sin2A is equal to ______.
Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`
If cos(α + β) = `(3/5)`, sin(α – β) = `5/13` and 0 < α, β < `π/4`, then tan (2α) is equal to ______.
If sinθ = `1/sqrt(2)` and `π/2 < θ < π`. Then the value of `(sinθ + cosθ)/tanθ` is ______.
In a right triangle PQR, right angled at Q. If tan P = `sqrt(3)`, then evaluate 2 sin P cos P.
Evaluate: 5 cosec2 45° – 3 sin2 90° + 5 cos 0°.
