English Medium कक्षा १० - CBSE Question Bank Solutions

If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p² – 1) = 2p

If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`

`"If "\frac{\cos \alpha }{\cos \beta }=m\text{ and }\frac{\cos \alpha }{\sin \beta }=n " show that " (m^2 + n^2 ) cos^2 β = n^2`

If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m²+n²=a²+b²

If acosθ – bsinθ = c, prove that asinθ + bcosθ = `\pm \sqrt{a^{2}+b^{2}-c^{2}`

Prove that: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`

If sinθ + sin² θ = 1, prove that cos² θ + cos⁴ θ = 1

Prove that `\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }+\frac{\sin\theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{2}{2\sin^{2}\theta -1}`

Express the ratios cos A, tan A and sec A in terms of sin A.

Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec² θ = 1 + tan² θ.

Solve the following pair of linear equation by the elimination method and the substitution method:

x + y = 5 and 2x – 3y = 4

Solve the following pair of linear equation by the elimination method and the substitution method: 

3x + 4y = 10 and 2x – 2y = 2

Solve the following pair of linear equation by the elimination method and the substitution method.

3x – 5y – 4 = 0 and 9x = 2y + 7

Solve the following pair of linear equation by the elimination method and the substitution method.

`x/2 + (2y)/3 = -1 and x - y /3 = 3`

Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes `1/2` if we only add 1 to the denominator. What is the fraction?

Form the pair of linear equation in the following problem, and find its solutions (if they exist) by the elimination method:

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.

Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Evaluate

`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`