Advertisements
Advertisements
प्रश्न
Evaluate the Following
4(sin4 60° + cos4 30°) − 3(tan2 60° − tan2 45°) + 5 cos2 45°
Advertisements
उत्तर
4(sin4 60° + cos4 30°) − 3(tan2 60° − tan2 45°) + 5 cos2 45° ........(i)
By trigonometric ratios we have
`sin 60^@ = sqrt3/2 - cos 30^@(sqrt3/2) tan 60^@ = sqrt3 tan 45^@ = 1 cos 45^@ = 1/sqrt2`
By substituting above values in (i), we get
`4([sqrt3/2]^4) + [sqrt3/2]^4) - 3([3]^2 - [1]^2) + `5[1/sqrt2]^2`
`=> 4[9/16 + 9/16] - 3[3 - 1]+ 5[1/2]`
`=> 4. 18/16 - 6 + 5/2`
`=> 1/4 - 6 + 5/2`
`=> 1/4 - 6 + 5/2`
`= 9/2 + 5/2 - 6`
`= 14/2 - 6 = 7 - 6 = 1`
संबंधित प्रश्न
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin A, cos A
Prove that `(sin "A" - 2sin^3 "A")/(2cos^3 "A" - cos "A") = tan "A"`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos A = 4/5`
If 3 tan θ = 4, find the value of `(4cos theta - sin theta)/(2cos theta + sin theta)`
If `tan theta = 1/sqrt7` `(cosec^2 theta - sec^2 theta)/(cosec^2 theta + sec^2 theta) = 3/4`
if `sec A = 17/8` verify that `(3 - 4sin^2A)/(4 cos^2 A - 3) = (3 - tan^2 A)/(1 - 3 tan^2 A)`
If `sin theta = a/b` find sec θ + tan θ in terms of a and b.
If Cosec A = 2 find `1/(tan A) + (sin A)/(1 + cos A)`
Evaluate the following
cos 60° cos 45° - sin 60° ∙ sin 45°
Evaluate the Following
`sin 30^2/sin 45^@ + tan 45^@/sec 60^@ - sin 60^@/cot 45^@ - cos 30^@/sin 90^@`
Find the value of x in the following :
`2sin 3x = sqrt3`
Find the value of x in the following :
`sqrt3 sin x = cos x`
If sin 2A = `1/2` tan² 45° where A is an acute angle, then the value of A is ______.
`(sin theta)/(1 + cos theta)` is ______.
The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is ______.
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
Find the value of sin 0° + cos 0° + tan 0° + sec 0°.
In the given figure, if sin θ = `7/13`, which angle will be θ?
Find will be the value of cos 90° + sin 90°.
