HSC Science (Computer Science) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions

Prove the following:

2(sin⁶θ + cos⁶θ) – 3(sin⁴θ + cos⁴θ) + 1 = 0

Prove the following:

cos⁴θ − sin⁴θ +1= 2cos²θ

Prove the following:

sin⁴θ +2sin²θ . cos²θ = 1 − cos⁴θ

Prove the following:

`(sin^3theta + cos^3theta)/(sintheta + costheta) + (sin^3theta - cos^3theta)/(sintheta - costheta)` = 2

Prove the following:

tan²θ − sin²θ = sin⁴θ sec²θ

Prove the following:

(sinθ + cosecθ)² + (cosθ + secθ)² = tan²θ + cot²θ + 7

Prove the following:

sin⁸θ − cos⁸θ = (sin²θ − cos²θ) (1 − 2 sin²θ cos²θ)

Prove the following:

sin⁶A + cos⁶A = 1 − 3sin²A + 3 sin⁴A

Prove the following:

(1 + tanA · tanB)² + (tanA − tanB)² = sec²A · sec²B

Prove the following:

`(1 + cottheta  +  "cosec" theta)/(1 - cottheta  +  "cosec" theta) = ("cosec" theta  + cottheta - 1)/(cottheta - "cosec"theta + 1)`

Prove the following:

`(tantheta + sectheta - 1)/(tantheta + sectheta + 1) = tantheta/(sec theta + 1)`

Prove the following:

`("cosec"theta + cottheta + 1)/(cottheta + "cosec" theta - 1) = cottheta/("cosec"theta - 1)`

Prove the following:

`("cosec"theta + cottheta - 1)/( "cosec"theta + cot theta + 1) =(1-sintheta)/costheta`

Express the following as a sum or difference of two trigonometric function:

`2sin  (2pi)/3 cos  pi/2`

Find the area of triangle whose vertices are

A(5, 8), B(5, 0) C(1, 0)

Find the area of triangle whose vertices are

`"P"(3/2, 1), "Q"(4, 2), "R"(4, (-1)/2)`

Find the area of triangle whose vertices are

M(0, 5), N(−2, 3), T(1, −4)

Find the area of quadrilateral whose vertices are 

A(−3, 1), B(−2, −2), C(3, -1), D(1, 4)

Find the value of k, if the area of triangle whose vertices are P(k, 0), Q(2, 2), R(4, 3) is `3/2 "sq.unit"`

Examine the collinearity of the following set of point:

A(3, −1), B(0, −3), C(12, 5)