Advertisements
Advertisements
Question
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Advertisements
Solution
`tan (pi/4 + theta) - tan(pi/4 - theta)` = `(tan pi/4 + tan theta)/(1 - tan pi/4 tan theta) - (tan pi/4 - tan theta)/(1 + tan pi/4 tan theta)`
= `(1 + tan theta)/(1 - tan theta) - (1 - tan theta)/(1 + tan theta)`
= `((1 + tan theta)^2 - (1 - tan theta)^2)/((1 - tan theta) (1 + tan theta))`
= `((1 + 2 tan theta + tan^2theta) - (1 - 2 tan theta + tan^2theta))/(1 - tan^2theta)`
= `(1 + 2 tan theta + tan^2theta - 1 + 2tan theta - tan^2theta)/(1 - tan^2theta)`
= `(4 tan theta)/(1 - tan^2theta)`
= `2 * (2 tan theta)/(1 - tan^2theta)`
= 2 tan 2θ
APPEARS IN
RELATED QUESTIONS
Find the values of sin (– 1110°)
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2` find the value of sin(x + y)
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Express the following as a sum or difference
2 sin 10θ cos 2θ
Express the following as a sum or difference
cos 5θ cos 2θ
Express the following as a product
cos 65° + cos 15°
Express the following as a product
cos 35° – cos 75°
Show that sin 12° sin 48° sin 54° = `1/8`
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
If A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
