SSC (English Medium) १० वीं कक्षा - Maharashtra State Board Question Bank Solutions

Prove that:

Sin⁴θ - cos⁴θ = 1 - 2cos²θ

In a trapezium ABCD, seg AB || seg DC seg BD ⊥ seg AD, seg AC ⊥ seg BC, If AD = 15, BC = 15 and AB = 25. Find A(▢ABCD)

Prove that:

`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.

Prove that:

`"tanθ"/("secθ"  –  1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`

The radius of a circle is 10 cm. The measure of an arc of the circle is 54^°. Find the area of the sector associated with the arc. (\[\pi\]= 3.14 )

The measure of an arc of a circle is 80° and its radius is 18 cm. Find the length of the arc. (π = 3.14)

Area of a sector of a circle of radius 15 cm is 30 cm² . Find the length of the arc of the sector.

If sin θ = `11/61`, find the values of cos θ using trigonometric identity.

Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`

The area of a sector of a circle of 6 cm radius is 15 π sq. cm. Find the measure of the arc and the length of the arc corresponding to the sector.

In the given figure, seg AB is a chord of a circle with centre P. If PA = 8 cm and distance of chord AB from the centre P is 4 cm, find the area of the shaded portion. ( \[\pi\] = 3.14, \[\sqrt{3}\]= 1.73 )

In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region 

From the figure find the value of sinθ.

If `secθ = 25/7 ` then find tanθ.

In Δ ABC, if ∠ A = 65° ; ∠ B = 40° then find the measure of ∠ C.

Length of a rectangular tank is twice its breadth. If the
depth of the tank is 3 m and area of its four walls is 108 m2, find the
length of the tank.

If tanθ `= 3/4` then find the value of secθ.

Find the length of an arc if measure of the arc is 90° and its radius
is 14 cm.

Digonals of parallelogram WXYZ intersect at point O. If OY =5, find WY.

Simplify : 2 sin30 + 3 tan45.