Advertisements
Advertisements
प्रश्न
If 3 tan θ = 4, find the value of `(4cos theta - sin theta)/(2cos theta + sin theta)`
Advertisements
उत्तर
3 tan theta = 4 find `(4cos theta - sin theta)/(2cos theta + sin theta)` ....(i)
`tan theta = 4/3`
Dividing equation (i) with cos θ we get
`= ((4cos theta - sin theta)/cos theta)/((2 cos theta + sin theta)/cos theta) = (4 - tan theta)/(2 + tan theta) [∵ sin theta/cos theta = tan theta]`
`= (4 - tan theta)/(2 + tan theta) [∵ sin theta/cos theta = tan theta]`
`= (4 - 4/1)/(2 + 4/5)`
`= (12 - 4)/(6 + 4)`
`= 8/10`
`= 4/5`
APPEARS IN
संबंधित प्रश्न
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin C, cos C
Given sec θ = `13/12`, calculate all other trigonometric ratios.
State whether the following are true or false. Justify your answer.
cot A is the product of cot and A.
If 4 tan θ = 3, evaluate `((4sin theta - cos theta + 1)/(4sin theta + cos theta - 1))`
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 theta = 7/25`
If 3 cot θ = 2, find the value of `(4sin theta - 3 cos theta)/(2 sin theta + 6cos theta)`.
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^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:
(cosec2 45° sec2 30°)(sin2 30° + 4 cot2 45° − sec2 60°)
Find the value of x in the following :
`2 sin x/2 = 1`
`(sin theta)/(1 + cos theta)` is ______.
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
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)`
Find the value of sin 45° + cos 45° + tan 45°.
If b = `(3 + cot π/8 + cot (11π)/24 - cot (5π)/24)`, then the value of `|bsqrt(2)|` is ______.
If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2.
(3 sin2 30° – 4 cos2 60°) is equal to ______.
