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

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)`

Without using trigonometric identity , show that :

`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`

Without using trigonometric identity , show that :

`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`

Without using trigonometric identity , show that :

`sin(50^circ + θ) - cos(40^circ - θ) = 0`

Without using trigonometric identity , show that :

`cos^2 25^circ + cos^2 65^circ = 1`

Without using trigonometric identity , show that :

`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`

Use graph paper for this question.

(Take 2 cm = 1 unit along both x-axis and y-axis.)

Plot the points O(0, 0), A(–4, 4), B(–3, 0) and C(0, –3).

1. Reflect points A and B on the y-axis and name them A' and B' respectively. Write down their co-ordinates.
2. Name the figure OABCB'A'.
3. State the line of symmetry of this figure.

Use a graph paper for this question.

(Take 2 cm = 1 unit on both x and y axes)

1. Plot the following points: A(0, 4), B(2, 3), C(1, 1) and D(2, 0).
2. Reflect points B, C, D on the y-axis and write down their coordinates. Name the images as B', C', D' respectively.
3. Join the points A, B, C, D, D', C', B' and A in order, so as to form a closed figure. Write down the equation to the line about which if this closed figure obtained is folded, the two parts of the figure exactly coincide.

Construct a triangle BPC given BC = 5 cm, BP = 4 cm and .

i) complete the rectangle ABCD such that:
a) P is equidistant from AB and BCV
b) P is equidistant from C and D.
ii) Measure and record the length of AB.

Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.

1. Construct a ΔABC in which BC = 6.5 cm, ∠ABC = 60°, AB = 5 cm.
2. Construct the locus of points at a distance of 3.5 cm from A.
3. Construct the locus of points equidistant from AC and BC.
4. Mark 2 points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.

Evaluate:

sin² 34° + sin² 56° + 2 tan 18° tan 72° – cot² 30°

Prove that:

tan (55° + x) = cot (35° – x)

Prove that:

`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)` 

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