Advertisements
Advertisements
Question
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
Advertisements
Solution
θ + Φ = α, tan θ = k tan Φ
k = `tantheta/tanphi`
`("k" - 1)/("k" + 1) = (tan theta/tan phi - 1)/(tan theta/tan phi + 1)`
= `(tan theta - tan phi)/(tan theta + tan phi)`
= `(sin theta/cos theta - sin phi/cos phi)/(sintheta/costheta + sin phi/cos phi)`
= `(sintheta cosphi - costheta sinphi)/(sintheta cosphi + costheta sin phi)`
`("k" - 1)/("k" + 1) = (sin(theta - phi))/(sin(theta + phi))`
= `(sin(theta - phi))/sin alpha`
`sin (theta - phi) = ("k" - 1)/("k" + 1) sin alpha`
APPEARS IN
RELATED QUESTIONS
Find the values of sin (– 1110°)
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
Prove that cos(π + θ) = − cos θ
Find a quadratic equation whose roots are sin 15° and cos 15°
Prove that sin 105° + cos 105° = cos 45°
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Express the following as a sum or difference
sin 35° cos 28°
Express the following as a sum or difference
sin 4x cos 2x
Show that `cos pi/15 cos (2pi)/15 cos (3pi)/15 cos (4pi)/15 cos (5pi)/15 cos (6pi)/15 cos (7pi)/15 = 1/128`
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
