Advertisements
Advertisements
Question
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
Options
`2/3`
`1/3`
`1/2`
`3/4`
Solution
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to `underlinebb(1/2)`.
Explanation:
Given,
4 tanθ = 3
⇒ tanθ = `3/4` ...(i)
∴ `(4 sin theta - cos theta)/(4 sin theta + cos theta) = (4 sin theta/cos theta - 1)/(4 sin theta/cos theta + 1)` ...[Divide by cos θ in both numerator and denominator]
= `(4 tan theta - 1)/(4 tan theta + 1)` ...`[∵ tan theta = sin theta/cos theta]`
= `(4(3/4) - 1)/(4(3/4) + 1)` ...[Put the value from equation (i)]
= `(3 - 1)/(3 + 1)`
= `2/4`
= `1/2`
APPEARS IN
RELATED QUESTIONS
If cot θ =` 7/8` evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sec theta = 13/5`
If Cosec A = 2 find `1/(tan A) + (sin A)/(1 + cos A)`
Evaluate the following
cos2 30° + cos2 45° + cos2 60° + cos2 90°
Evaluate the Following
`cot^2 30^@ - 2 cos^2 60^circ- 3/4 sec^2 45^@ - 4 sec^2 30^@`
If sin (A − B) = sin A cos B − cos A sin B and cos (A − B) = cos A cos B + sin A sin B, find the values of sin 15° and cos 15°.
sin (45° + θ) – cos (45° – θ) is equal to ______.
If cos (40° + A) = sin 30°, then value of A is ______.
3 sin² 20° – 2 tan² 45° + 3 sin² 70° is equal to ______.
If sin θ + sin² θ = 1, then cos² θ + cos4 θ = ______.
