Advertisements
Advertisements
Question
Given that sinα = `1/2` and cosβ = `1/2`, then the value of (α + β) is ______.
Options
0°
30°
60°
90°
Advertisements
Solution
Given that sinα = `1/2` and cosβ = `1/2`, then the value of (α + β) is 90°.
Explanation:
Given,
sinα = `1/2` = sin30° ...`[∵ sin 30^circ = 1/2]`
⇒ α = 30°
And cosβ = `1/2` = cos60° ...`[∵ 60^circ = 1/2]`
⇒ β = 60°
∴ α + β = 30° + 60° = 90°
APPEARS IN
RELATED QUESTIONS
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin A, cos A
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.
cot A is the product of cot and A.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cos theta = 12/2`
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 `tan theta = 1/sqrt7` `(cosec^2 theta - sec^2 theta)/(cosec^2 theta + sec^2 theta) = 3/4`
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^@)`
If cos (81 + θ)° = sin`("k"/3 - theta)^circ` where θ is an acute angle, then the value of k is ______.
`(sin theta)/(1 + cos theta)` is ______.
Prove that sec θ + tan θ = `cos θ/(1 - sin θ)`.
Proof: L.H.S. = sec θ + tan θ
= `1/square + square/square`
= `square/square` ......`(∵ sec θ = 1/square, tan θ = square/square)`
= `((1 + sin θ) square)/(cos θ square)` ......[Multiplying `square` with the numerator and denominator]
= `(1^2 - square)/(cos θ square)`
= `square/(cos θ square)`
= `cos θ/(1 - sin θ)` = R.H.S.
∴ L.H.S. = R.H.S.
∴ sec θ + tan θ = `cos θ/(1 - sin θ)`
Prove that `tan θ/(1 - cot θ) + cot θ/(1 - tanθ)` = 1 + sec θ cosec θ
If f(x) = `3cos(x + (5π)/6) - 5sinx + 2`, then maximum value of f(x) is ______.
The maximum value of the expression 5cosα + 12sinα – 8 is equal to ______.
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 ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.
