Advertisements
Advertisements
प्रश्न
Find the value of x in the following :
`sqrt3 sin x = cos x`
Advertisements
उत्तर
We have
`sqrt3 sin x = cos x`
Now by cross multiplying we get,
`sqrt3 sin x = cos x``
`=> sin x/cos x = 1/sqrt3`.........(1)
Now we know that
`sin x/cos x = tan x` .......(2)
Therefore from equation (1) and (2)
We get
`tan x = 1/sqrt3` .......(3)
since
`tan 30^2 = 1/sqrt3` ....(4)
Therefore, by comparing equation (3) and (4) we get,
`x = 30^@`
Therefore
`x = 30^@`
APPEARS IN
संबंधित प्रश्न
Given sec θ = `13/12`, calculate all other trigonometric ratios.
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
If cot θ =` 7/8` evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`
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`
Evaluate the following
sin 45° sin 30° + cos 45° cos 30°
Evaluate the following
`2 sin^2 30^2 - 3 cos^2 45^2 + tan^2 60^@`
Evaluate the Following
`4/(cot^2 30^@) + 1/(sin^2 60^@) - cos^2 45^@`
Find the value of x in each of the following :
cos x = cos 60º cos 30º + sin 60º sin 30º
sin (45° + θ) – cos (45° – θ) is equal to ______.
The value of sin² 30° – cos² 30° is ______.
If cos A + cos² A = 1, then sin² A + sin4 A is equal to ______.
The value of the expression (sin 80° – cos 80°) is negative.
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
Let f(x) = sinx.cos3x and g(x) = cosx.sin3x, then the value of `7((f(π/7) + g(π/7))/(g((5π)/14) + f((5π)/14)))` is ______.
If `θ∈[(5π)/2, 3π]` and 2cosθ + sinθ = 1, then the value of 7cosθ + 6sinθ is ______.
Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.
(3 sin2 30° – 4 cos2 60°) is equal to ______.
In a right triangle PQR, right angled at Q. If tan P = `sqrt(3)`, then evaluate 2 sin P cos P.
