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
State whether the following are true or false. Justify your answer.
sin θ = `4/3`, for some angle θ.
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`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
tan θ = 11
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin theta = 11/5`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin theta = sqrt3/2`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
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)`
Evaluate the following
sin 45° sin 30° + cos 45° cos 30°
Evaluate the following
cos2 30° + cos2 45° + cos2 60° + cos2 90°
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
Find the value of x in the following :
cos 2x = cos 60° cos 30° + sin 60° sin 30°
If cosec θ - cot θ = `1/3`, the value of (cosec θ + cot θ) is ______.
If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is equal to ______.
In ΔABC, ∠ABC = 90° and ∠ACB = θ. Then write the ratios of sin θ and tan θ from the figure.
Prove that: cot θ + tan θ = cosec θ·sec θ
Proof: L.H.S. = cot θ + tan θ
= `square/square + square/square` ......`[∵ cot θ = square/square, tan θ = square/square]`
= `(square + square)/(square xx square)` .....`[∵ square + square = 1]`
= `1/(square xx square)`
= `1/square xx 1/square`
= cosec θ·sec θ ......`[∵ "cosec" θ = 1/square, sec θ = 1/square]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
`sqrt(3)` cos2A + `sqrt(3)` sin2A is equal to ______.
Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.
In ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.
