Advertisements
Advertisements
Question
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
Advertisements
Solution
L.H.S = `(cos("A" + 15^circ))/(sin("A" + 15^circ)) - (sin("A" - 15^circ))/(cos("A" - 15^circ))`
= `(cos("A" + 15^circ)cos("A" - 15^circ) - sin("A" + 15^circ)sin("A" - 15^circ))/(sin("A" + 15^circ) cos("A" - 15^circ))`
= `(cos("A" + 15^circ + "A" - 15^circ))/(1/2[sin("A" + 15^circ + "A" - 15^circ) + sin("A" + 15^circ - "A" + 15^circ)]`
= `(2cos2"A")/(sin2"A" + sin30^circ)`
= `(2cos2"A")/(1/2 + sin2"A")`
= `(4cos2"A")/(1 + 2sin 2"A")`
= R.H.S
APPEARS IN
RELATED QUESTIONS
Find the values of cos(300°)
Find the values of cot(660°)
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`
Find sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
Prove that sin 105° + cos 105° = cos 45°
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
