Advertisements
Advertisements
Question
If 3 tan θ = 4, find the value of `(4cos theta - sin theta)/(2cos theta + sin theta)`
Advertisements
Solution
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
RELATED QUESTIONS
If cot θ = `7/8` evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`.
In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
State whether the following are true or false. Justify your answer.
sin θ = `4/3`, for some angle θ.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin theta = sqrt3/2`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan theta = 8/15`
If Cosec A = 2 find `1/(tan A) + (sin A)/(1 + cos A)`
Evaluate the following
cos 60° cos 45° - sin 60° ∙ sin 45°
Evaluate the following
`2 sin^2 30^2 - 3 cos^2 45^2 + tan^2 60^@`
Evaluate the Following
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)
Evaluate the Following
`(sin 30^@ - sin 90^2 + 2 cos 0^@)/(tan 30^@ tan 60^@)`
Find the value of x in the following :
`2 sin x/2 = 1`
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
sin (45° + θ) – cos (45° – θ) is equal to ______.
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
The value of the expression (sin 80° – cos 80°) is negative.
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
Find will be the value of cos 90° + sin 90°.
If sin θ + cos θ = `sqrt(2)` then tan θ + cot θ = ______.
If b = `(3 + cot π/8 + cot (11π)/24 - cot (5π)/24)`, then the value of `|bsqrt(2)|` is ______.
If sin θ – cos θ = 0, then find the value of sin4 θ + cos4 θ.
