Advertisements
Advertisements
प्रश्न
Find the value of x in the following :
`sqrt3 tan 2x = cos 60^@ + sin45^@ cos 45^@`
Advertisements
उत्तर
We have
`sqrt3 tan 2x = cos 60^@ + sin45^@ cos 45^@` .......(1)
Now we know that
`sin 45^@ = cos 45^@ = 1/sqrt2 and cos 60^@ = 1/2`
Now by substituting above values in equation (1), we get,
`sqrt3 tan 2x = cos 60^@ + sin 45^@ cos 45^@`
`sqrt3 tan 2x = 1/2 + 1/sqrt2 xx 1/sqrt2`
`= 1/2 + 1/(sqrt2 xx sqrt2)`
`=1/2 + 1/2`
`= (1 + 1)/2`
`= 2/2`
= 1
Therefore,
`sqrt3 tan 2x = 1`
`=> tan 2x = 1/sqrt3` .....(2)
Since
`tan 30^@ = 1/sqrt3` .....(3)
Therefore by comparing equation (2) and (3)
We get
`2x = 30^@`
`x = 30^@/2`
`=> x = 15^@`
x = 15
APPEARS IN
संबंधित प्रश्न
In ΔABC, right angled at B. If tan A = `1/sqrt3` , find the value of
- sin A cos C + cos A sin C
- cos A cos C − sin A sin C
State whether the following are true or false. Justify your answer.
cot A is the product of cot and A.
Prove that `(sin "A" - 2sin^3 "A")/(2cos^3 "A" - cos "A") = tan "A"`
If `tan theta = 24/7`, find that sin 𝜃 + cos 𝜃
Evaluate the following
cos 60° cos 45° - sin 60° ∙ sin 45°
Evaluate the following
`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°`
Evaluate the Following
4(sin4 30° + cos2 60°) − 3(cos2 45° − sin2 90°) − sin2 60°
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
Find the value of x in the following :
`2 sin x/2 = 1`
Find the value of x in each of the following :
cos x = cos 60º cos 30º + sin 60º sin 30º
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
The value of sin² 30° – cos² 30° is ______.
If cos (40° + A) = sin 30°, then value of A is ______.
If cos A + cos² A = 1, then sin² A + sin4 A is equal to ______.
If sin θ + sin² θ = 1, then cos² θ + cos4 θ = ______.
In ΔABC, ∠ABC = 90° and ∠ACB = θ. Then write the ratios of sin θ and tan θ from the figure.
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)`
What will be the value of sin 45° + `1/sqrt(2)`?
If sin θ – cos θ = 0, then find the value of sin4 θ + cos4 θ.
In ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.
