Advertisements
Advertisements
प्रश्न
Evaluate the Following
4(sin4 30° + cos2 60°) − 3(cos2 45° − sin2 90°) − sin2 60°
Advertisements
उत्तर
4(sin4 30° + cos2 60°) − 3(cos2 45° − sin2 90°) − sin2 60° .....(i)
By trigonometric ratios we have
`sin 30^@ = 1/2 cos 60^@ = 1/2 cos 45^@ = 1/sqrt2 sin 90^@ = 1 sin 60^@ = sqrt3/2`
By substituting above values in (i), we get
`(4[(1/2)^4 + (1/2)^2]) - 3[[1/sqrt2]^2 - 1] - [sqrt3/2]^2`
`4[1/16 + 1/4] - 3[(1 - [sqrt2])/(sqrt2)^2] - 3/4`
`= 1/4 + 1 - 3/4 + 3/2 = 2`
APPEARS IN
संबंधित प्रश्न
State whether the following are true or false. Justify your answer.
The value of tan A is always less than 1.
State whether the following are true or false. Justify your answer.
sin θ = `4/3`, for some angle θ.
If 4 tan θ = 3, evaluate `((4sin theta - cos theta + 1)/(4sin theta + cos theta - 1))`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan theta = 8/15`
If `cos θ = 12/13`, show that `sin θ (1 - tan θ) = 35/156`.
If `tan theta = 1/sqrt7` `(cosec^2 theta - sec^2 theta)/(cosec^2 theta + sec^2 theta) = 3/4`
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
if `sin theta = 3/4` prove that `sqrt(cosec^2 theta - cot)/(sec^2 theta - 1) = sqrt7/3`
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
Find the value of x in the following :
`2sin 3x = sqrt3`
If `sqrt2 sin (60° – α) = 1` then α is ______.
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
Prove the following:
If tan A = `3/4`, then sinA cosA = `12/25`
The value of the expression (sin 80° – cos 80°) is negative.
Find the value of sin 45° + cos 45° + tan 45°.
What will be the value of sin 45° + `1/sqrt(2)`?
If b = `(3 + cot π/8 + cot (11π)/24 - cot (5π)/24)`, then the value of `|bsqrt(2)|` is ______.
If `θ∈[(5π)/2, 3π]` and 2cosθ + sinθ = 1, then the value of 7cosθ + 6sinθ is ______.
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.
