HSC Science (Computer Science) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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)

Examine the collinearity of the following set of point:

P(3, −5), Q(6, 1), R(4, 2)

Examine the collinearity of the following set of point:

`"L"(0, 1/2), "M"(2, -1), "N"(-4, 7/2)`

Select the correct option from the given alternatives:

If A(0,0), B(1,3) and C(k,0) are vertices of triangle ABC whose area is 3 sq.units then value of k is

Answer the following question:

Find the area of triangle whose vertices are A(−1, 2), B(2, 4), C(0, 0)

Answer the following question:

Find the area of triangle whose vertices are P(3, 6), Q(−1, 3), R(2, −1)