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

Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.

Prove that identity:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`

Prove that:  `1/(sec θ - tan θ) = sec θ + tan θ`.

Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.

Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`

Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.

Prove that: `(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(sin^2 A - cos^2 A)`.

Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`

Prove that: sin⁶θ + cos⁶θ = 1 - 3sin²θ cos²θ. 

Prove that:
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`

Prove that sin² 5° + sin² 10° .......... + sin² 85° + sin² 90° = `9 1/2`.

Prove that : `tan"A"/(1 - cot"A") + cot"A"/(1 - tan"A") = sec"A".cosec"A" + 1`.

Following table present educational level (middle stage) of females in Arunachal pradesh according to 1981 census:

Draw a histogram to represent the above data.

Distribution of height in cm of 100 people is given below:

Draw a histogram to represent the above data.

The time taken, in seconds, to solve a problem for each of 25 persons is as follows:

(i) Construct a frequency distribution for these data using a class interval of 10 seconds.
(ii) In a school the weekly pocket money of 50 students is as follow's:

Draw a histogram and a frequency polygon on the same graph. Find mode from the graph.

Draw a histogram and frequency polygon to represent the following data (on the same scale) which shows the monthly cost of living index of a city in a period of 2 years:

Draw the histogram for the following frequency distribution and hence estimate the mode for the distribution.

Draw a histogram to represent the following data:

(Use a graph paper for this question.) The daily pocket expenses of 200 students in a school are given below:

Draw a histogram representing the above distribution and estimate the mode from the graph.

Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 5x² – 1x + 4