(English Medium) ICSE Class 10 - CISCE Question Bank Solutions

If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1

If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`

If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn 

If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`

If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)

Without using trigonometric table , evaluate : 

`cosec49°cos41° + (tan31°)/(cot59°)`

Without using trigonometric table , evaluate : 

`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`

Without using trigonometric table , evaluate : 

`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`

Without using trigonometric table , evaluate : 

`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`

Without using trigonometric table , evaluate : 

`sin72^circ/cos18^circ  - sec32^circ/(cosec58^circ)`

Find the value of `θ(0^circ < θ < 90^circ)` if : 

`tan35^circ cot(90^circ - θ) = 1`

Find the value of `θ(0^circ < θ < 90^circ)` if : 

`cos 63^circ sec(90^circ - θ) = 1`

prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`

Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A

Find x , if `cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`

Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`

Prove that  `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`

For ΔABC , prove that : 

`tan ((B + C)/2) = cot "A/2`

For ΔABC , prove that : 

`sin((A + B)/2) = cos"C/2`

Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`