Advertisements
Advertisements
Question
Evaluate the following
sin2 30° + sin2 45° + sin2 60° + sin2 90°
Advertisements
Solution
sin2 30° + sin2 45° + sin2 60° + sin2 90° .....(1)
`sin 30^@ = 1/2 sin 45^@ = 1/sqrt2`
`sin 60^@ = sqrt3/2 sin 90^@ = 1`
By substituting above values in (i), we get
`= [1/2]^2 + [1/sqrt2]^2 + [sqrt3/2]^2 + [1]^2`
`= 1/4 + 1/2 + 3/4 + 1 => (1 + 3)/4 + (1 + 2)/2`
`=> 1 + 3/2 = (2 + 3)/2 = 5/2`
APPEARS IN
RELATED QUESTIONS
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos theta = 7/25`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cot theta = 12/5`
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)`
If `cot theta = 1/sqrt3` show that `(1 - cos^2 theta)/(2 - sin^2 theta) = 3/5`
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
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
4(sin4 60° + cos4 30°) − 3(tan2 60° − tan2 45°) + 5 cos2 45°
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
Evaluate the Following
`4/(cot^2 30^@) + 1/(sin^2 60^@) - cos^2 45^@`
Evaluate the Following:
`(tan^2 60^@ + 4 cos^2 45^@ + 3 sec^2 30^@ + 5 cos^2 90)/(cosec 30^@ + sec 60^@ - cot^2 30^@)`
Find the value of x in the following :
`2 sin x/2 = 1`
Find the value of x in the following :
`sqrt3 sin x = cos x`
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
sin (45° + θ) – cos (45° – θ) is equal to ______.
If cos (40° + A) = sin 30°, then value of A is ______.
Find will be the value of cos 90° + sin 90°.
Prove that `tan θ/(1 - cot θ) + cot θ/(1 - tanθ)` = 1 + sec θ cosec θ
In a right triangle PQR, right angled at Q. If tan P = `sqrt(3)`, then evaluate 2 sin P cos P.
