Advertisements
Advertisements
प्रश्न
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
उत्तर
`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
संबंधित प्रश्न
Find the values of cos(300°)
Find the values of `tan ((19pi)/3)`
`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
Prove that sin(π + θ) = − sin θ.
Find a quadratic equation whose roots are sin 15° and cos 15°
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "C"/2`
If A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
Choose the correct alternative:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is
