Advertisements
Advertisements
Question
Prove that sin 75° – sin 15° = cos 105° + cos 15°
Solution
R.H.S = cos 105° + cos 15°
= cos(90° + 15°) + cos(90° – 75°)
= – sin 15° + sin 75°
= sin 75° – sin 15°
= L.H.S
APPEARS IN
RELATED QUESTIONS
Find the values of cos(300°)
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II 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 A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)
Find cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2` and sin y = `- 24/25` with `pi < y < (3pi)/2`
Find a quadratic equation whose roots are sin 15° and cos 15°
Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`
Show that tan 75° + cot 75° = 4
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
If A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
Choose the correct alternative:
If `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
