(English Medium) ICSE Class 10 - CISCE Important Questions

Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`

Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`

Evaluate without using trigonometric tables:

`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`

As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.

Prove that `(tan^2 theta)/(sec theta - 1)^2 = (1 + cos theta)/(1 - cos theta)`

Prove that (cosec A – sin A)(sec A – cos A) sec² A = tan A.

Without using trigonometric tables evaluate

`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80^@)`

Prove that: 
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1

Simplify 

sin A `[[sinA   -cosA],["cos A"  " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`

Prove that:

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

tan θ × `sqrt(1 - sin^2 θ)` is equal to:

(1 + sin A)(1 – sin A) is equal to ______.

Prove the following identity:

(sin²θ – 1)(tan²θ + 1) + 1 = 0

Statement 1: sin²θ + cos²θ = 1

Statement 2: cosec²θ + cot²θ = 1

Which of the following is valid?

Factorize: sin³θ + cos³θ

Hence, prove the following identity:

`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`

The daily wages of 80 workers in a project are given below.

Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs. 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate:

1. the median wage of the workers.
2. the lower quartile wage of workers.
3. the numbers of workers who earn more than Rs. 625 daily.

The histogram below represents the scores obtained by 25 students in a mathematics mental test. Use the data to:

1. Frame a frequency distribution table.
2. To calculate mean.
3. To determine the Modal class.

The weight of 50 workers is given below:

Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following:

1) The upper and lower quartiles.

2) If weighing 95 kg and above is considered overweight, find the number of workers who are overweight.

The marks obtained by 100 students in a Mathematics test are given below:

Draw an ogive for the given distribution on a graph sheet.

Use a scale of 2 cm = 10 units on both axes.

Use the ogive to estimate the:

1) Median.

2) Lower quartile.

3) A number of students who obtained more than 85% marks in the test.

4) A number of students who did not pass in the test if the pass percentage was 35.

A Mathematics aptitude test of 50 students was recorded as follows:

Draw a histogram from the above data using a graph paper and locate the mode.