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

Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ

If cos A = `(2sqrt("m"))/("m" + 1)`, then prove that cosec A = `("m" + 1)/("m" - 1)`

Prove that sin⁶A + cos⁶A = 1 – 3sin²A . cos²A

Prove that 2(sin⁶A + cos⁶A) – 3(sin⁴A + cos⁴A) + 1 = 0

Prove that `"cot A"/(1 - tan "A") + "tan A"/(1 - cot"A")` = 1 + tan A + cot A = sec A . cosec A + 1

If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3

If cos A + cos²A = 1, then sin²A + sin4 A = ?

If cosec A – sin A = p and sec A – cos A = q, then prove that `("p"^2"q")^(2/3) + ("pq"^2)^(2/3)` = 1

Show that tan 7° × tan 23° × tan 60° × tan 67° × tan 83° = `sqrt(3)`

If sin θ + cos θ = `sqrt(3)`, then show that tan θ + cot θ = 1

If tan θ – sin²θ = cos²θ, then show that sin² θ = `1/2`.

Prove that (1 – cos²A) . sec²B + tan²B(1 – sin²A) = sin²A + tan²B

Complete the following activity to prove:

cotθ + tanθ = cosecθ × secθ

Activity: L.H.S. = cotθ + tanθ

= `cosθ/sinθ + square/cosθ`

= `(square + sin^2theta)/(sinθ xx cosθ)`

= `1/(sinθ xx  cosθ)` ....... ∵ `square`

= `1/sinθ xx 1/cosθ`

= `square xx secθ`

∴ L.H.S. = R.H.S.

If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.

Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`

If x = `θ/360` × 2πr then what is x in the formula?

In the given figure, a rectangle ABCD is inscribed inside a semi-circle of radius 10 cm. Using the dimensions given in the figure, determine the area of the shaded region.

The perimeter of an arc of radius 4.2 cm is 12.8 cm. Determine the angle subtended by the arc at the centre of circle.

In an isosceles triangle PQR, the length of equal sides PQ and PR is 13 cm and base QR is 10 cm. Find the length of perpendicular bisector drawn from vertex P to side QR.

In the adjoining figure, a tangent is drawn to a circle of radius 4 cm and centre C, at the point S. Find the length of the tangent ST, if CT = 10 cm.