Download App

Transformation Formulae — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTransformation Formulae4 Marks
Question
Prove that: $\text{If}\cos\text{A}+\cos\text{B}=\frac{1}{2}\text{ and }\sin\text{A}+\sin\text{B}=\frac{1}{4},$ prove that $\tan\Big(\frac{\text{A+B}}{2}\Big)=\frac{1}{2}.$
✓

Answer

We have, $\text{LHS}=\cos\text{A}+\cos\text{B}=\frac{1}{2}$ $\text{and},\ \sin\text{A}+\sin\text{B}=\frac{1}{4}$ Now, $\frac{\sin\text{A}+\sin\text{B}}{\cos\text{A}+\cos\text{B}}=\frac{\frac{1}{4}}{\frac{1}{2}}$ [On dividing] $\Rightarrow\ \frac{2\sin\Big(\frac{\text{A}+\text{B}}{2}\Big)\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)}{2\cos\Big(\frac{\text{A}+\text{B}}{2}\Big)\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)}=\frac{1}{2}$ $\Rightarrow\ \frac{\sin\Big(\frac{\text{A}+\text{B}}{2}\Big)}{\cos\Big(\frac{\text{A}+\text{B}}{2}\Big)}=\frac{1}{2}$ $\Rightarrow\ \tan\Big(\frac{\text{A}+\text{B}}{2}\Big)=\frac{1}{2}$ $\Rightarrow\ \text{RHS}$ Hence proved.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 4 marks)" from Transformation Formulae→Transformation Formulae — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the equation of the hyperbola whose foci are (4, 2) and (8,2) and eccentricity is 2.
→
A farmer buys a used tractor for ₹ 12000. He pays ₹ 6000 cash and agrees to pay the balance in annual instalments of ₹ 500 plus 12% interest on the unpaid amount. How much the tractor cost him?
→
Differentiate the following functions with respect to x:$\frac{\sin\text{x}-\text{x}\cos\text{x}}{\text{x}\sin\text{x}+\cos\text{x}}$
→
Find the equation of an ellipse whose axes lie along coordinate axes and which passes through (4, 3) and (-1, 4).
→
Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. $16x^2 - 9y^2 = 576$
→
Verify the following: (–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are the vertices of a parallelogram.
→
If $\alpha={^\text{m}}\text{C}_{2},$ then find the value of ${^{\alpha}}\text{C}_{2}.$
→
An arch is in the form of a parabola with its axis vertical. The arch is $10m$ high and 5m wide at the base. How wide is it $2m$ from the vertex of the parabola?
→
Let A and B be two stes such that: $\text{n(P)} = 20, \text{n(A}\cup\text{B)=42 and n(A}\cap\text{B})=4.$ Find: $\text{n(A} - \text{B)}.$
→
For some constants a and b, find the derivative of$(\text{a}\text{x}^2+\text{b})^2$
→