SSC (English Medium) १० वीं कक्षा - Maharashtra State Board Question Bank Solutions for Geometry Mathematics 2

Prove that cosec θ – cot θ = `sin theta/(1 + cos theta)`

Prove that `(1 + sec "A")/"sec A" = (sin^2"A")/(1 - cos"A")`

Prove that `(1 + sin "B")/"cos B" + "cos B"/(1 + sin "B")` = 2 sec B

Prove that

sin²A . tan A + cos²A . cot A + 2 sin A . cos A = tan A + cot A

Prove that

sec²A – cosec²A = `(2sin^2"A" - 1)/(sin^2"A"*cos^2"A")`

Prove that

`(cot "A" + "cosec  A" - 1)/(cot"A" - "cosec  A" + 1) = (1 + cos "A")/"sin A"`

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.