HSC Science (General) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Find the value of :

cosec 780°

Find the value of :

cot (– 1110°)

Prove the following:

`(cos(pi + x) cos(-x))/(sin(pi - x)cos(pi/2 + x))` = cot²x

Prove the following:

`cos((3pi)/2 + x) cos(2pi + x)[cot((3pi)/2 - x) + cot(2pi + x)]` = 1

Prove the following:

sec 840° . cot (– 945°) + sin 600° tan (– 690°) = `3/2`

Prove the following:

`("cosec"(90^circ - x)sin(180^circ - x)cot(360^circ - x))/(sec(180^circ + x)tan(90^circ + x)sin(-x))` = 1

Prove the following:

`(sin^3(pi + x)sec^2(pi - x)tan(2pi - x))/(cos^2(pi/2 + x)sin(pi - x)"cosec"^2 - x)` = tan³x

Prove the following:

cosθ + sin (270° + θ) − sin (270° − θ) + cos (180° + θ) = 0

Select the correct option from the given alternatives :

If sin θ = n sin (θ + 2α), then tan (θ + α) is equal to

Select the correct option from the given alternatives :

Let 0 < A, B < `pi/2` satisfying the equation 3 sin²A + 2 sin²B = 1 and 3 sin 2A − 2 sin 2B = 0 then A + 2B is equal to ______

Prove the following:

tan 20° tan 80° cot 50° = `sqrt(3)`

Prove the following:

cosec 48° + cosec 96° + cosec 192° + cosec 384° = 0

Prove the following:

sin 20° sin 40° sin 80° = `sqrt(3)/8`

Prove the following:

sin 18° = `(sqrt(5) - 1)/4`

Prove the following:

cos 36° = `(sqrt(5) + 1)/4`

Prove the following:

sin 36° = `(sqrt(10 - 2sqrt(5)))/4`

Prove the following:

`tan  pi/8 = sqrt(2) - 1`

Prove the following:

tan6° tan42° tan66° tan78° = 1

Prove the following:

sin47° + sin61° − sin11° − sin25° = cos7°

A box contains 10 red balls and 15 green balls. Two balls are drawn in succession without replacement. What is the probability that, one is red and the other is green?