English Medium कक्षा १० - CBSE Important Questions

If `tan theta = 24/7`, find that sin θ + cos θ.

Prove the following trigonometric identities.

`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`

Prove the following trigonometric identities.

`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`

`1/((1+ sin θ)) + 1/((1 - sin θ)) = 2 sec^2 θ`

cos⁴ A − sin⁴ A is equal to ______.

(sec A + tan A) (1 − sin A) = ______.

Find the value of ( sin² 33° + sin² 57°).

Prove that :(sinθ+cosecθ)²+(cosθ+ secθ)² = 7 + tan² θ+cot² θ.

Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2. 

Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`

Evaluate:
`(tan 65°)/(cot 25°)`

Prove that (sin θ + cosec θ)² + (cos θ + sec θ)² = 7 + tan² θ + cot² θ. 

If sec θ = x + `1/(4"x"), x ≠ 0,` find (sec θ + tan θ)

Evaluate:

`(tan 65^circ)/(cot 25^circ)`

Prove that:
`sqrt(( secθ - 1)/(secθ + 1)) + sqrt((secθ + 1)/(secθ - 1)) = 2 "cosec"θ`

Prove that:

`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`

If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`

Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`

If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p² – 1) = 2p.

If sin A = `1/2`, then the value of sec A is ______.