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

Prove the following identity : 

`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`

Prove the following identity : 

`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`

Prove the following identity :

`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`

Prove the following identity  :

`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`

Prove the following identity : 

`sec^4A - sec^2A = sin^2A/cos^4A`

Draw a straight line AB of 9 cm. Draw the locus of all points which are equidistant from A and B. Prove your statement. 

Two straight roads AB and CD cross each other at Pat an angle of 75°  . X is a stone on the road AB, 800m from P towards B. BY taking an appropriate scale draw a figure to locate the position of a pole, which is equidistant from P and X, and is also equidistant from the roads. 

Prove the following identity : 

`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`

Draw two intersecting lines to include an angle of 30°. Use ruler and compasses to locate points which are equidistant from these Iines and also 2 cm away from their point of intersection. How many such points exist? 

Prove the following identity : 

`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`

Prove the following identity : 

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

Prove the following identity : 

`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`

AB and CD are two intersecting lines. Find a point equidistant from AB and CD, and also at a distance of 1.8 cm from another given line EF. 

Without using set squares or protractor, construct a quadrilateral ABCD in which ∠ BAD = 45°, AD = AB = 6 cm, BC= 3.6 cm and CD=5 cm. Locate the point P on BD which is equidistant from BC and CD. 

Construct a rhombus ABCD with sides of length 5 cm and diagonal AC of length 6 cm. Measure ∠ ABC. Find the point R on AD such that RB = RC. Measure the length of AR. 

Prove the following identity : 

`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`

Construct a rhombus ABCD whose diagonals AC and BD are 8 cm and 6 cm respectively. Find by construction a point P equidistant from AB and AD and also from C and D. 

Construct a ti.PQR, in which PQ=S. 5 cm, QR=3. 2 cm and PR=4.8 cm. Draw the locus of a point which moves so that it is always 2.5 cm from Q. 

Construct a Δ XYZ in which XY= 4 cm, YZ = 5 cm and ∠ Y = 1200. Locate a point T such that ∠ YXT is a right angle and Tis equidistant from Y and Z. Measure TZ. 

In  Δ PQR, s is a point on PR such that ∠ PQS = ∠  RQS . Prove thats is equidistant from PQ and QR.