HSC Science Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

`(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 = `- 1/2`, θ lies in the III quadrant

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

Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant

Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV 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

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

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)

If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of cos(x − y)

If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of tan(x + y)

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)

If sin A = `3/5` and cos B = `9/41, 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of cos(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 sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`

Find the value of cos 105°.

Find the value of sin105°.

Find the value of tan `(7pi)/12`

Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`