Download App

Trigonometric Ratios of Multiple and Submultiple Angles — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios of Multiple and Submultiple Angles1 Mark
Question
If $\frac{\cos(\text{x - y})}{\cos(\text{x+y})}=\frac{\text{m}}{\text{n}},$ then write the value of $\tan\text{x}\tan\text{y}.$
✓

Answer

We have, $\frac{\cos(\text{x - y})}{\cos(\text{x+y})}=\frac{\text{m}}{\text{n}}$ $\Rightarrow\frac{\cos\text{x}\cos\text{y}+\sin\text{x}\sin\text{y}}{\cos\text{x}\cos\text{y}-\sin\text{x}\sin\text{y}}=\frac{\text{m}}{\text{n}}$ $\Rightarrow\frac{\frac{\cos\text{x}\cos\text{y}+}{\cos\text{x}\cos\text{y}}+\frac{\sin\text{x}\sin\text{y}}{\cos\text{x}\cos\text{y}}}{\frac{\cos\text{x}\cos\text{y}}{\cos\text{x}\cos\text{y}}-\frac{\sin\text{x}\sin\text{y}}{\cos\text{x}\cos\text{y}}}=\frac{\text{m}}{\text{n}}$ $[$Dividing and multiplying numerator and denominator by $\cos\text{x}\cos\text{y}]$ $\Rightarrow\frac{1+\tan\text{x}\tan\text{y}}{1-\tan\text{x}\tan\text{y}}=\frac{\text{m}}{\text{n}}$ $\Rightarrow\text{n+n}\tan\text{x}\tan\text{y}=\text{m - m}\tan\text{x}\tan\text{y}$ $\Rightarrow\tan\text{x}\tan\text{y}(\text{n+m})=\text{m - n}$ $\Rightarrow\tan\text{x}\tan\text{y}=\frac{\text{m - n}}{\text{m+n}}$

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 1 marks)" from Trigonometric Ratios of Multiple and Submultiple Angles→Trigonometric Ratios of Multiple and Submultiple Angles — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\frac{(\text{a}^2+1)^2}{2\text{a}-\text{i}}=\text{x}+\text{iy},$ find the value of $\text{x}^2+\text{y}^2.$
→
Write the domain and range of $\text{f(x)}=\sqrt{\text{x}-[\text{x}]}$
→
Write the maximum number of points of intersection of 8 straight lines in a plane.
→
If x $\in$A and A $\in$B , then x $\in$B.If it is true, prove it. If it is false, give an example.
→
There are 200 individualwith a skin disorder, 120 has been exposed to chemical $C_1, 50$ to chemical $C_2$ and 30 to both the chemicals $C_1$ and $C_2$. Find the number of individualexposed to chemical $C_1$ or chemical $C_2$
→
Write each of the following statements in the form “if-then” A quadrilateral is a parallelogram if its diagonals bisect each other.
→
Write the value of $\lim_\limits{\text{x}\rightarrow\text{a}}\frac{\text{xf}(\text{a})-\text{af}(\text{x})}{\text{x}-\text{a}}$
→
Write the set of all vowels in the English alphabet which precede q.
→
Express the following as the sum or difference of sines and cosines: $2\cos7\text{x}\cos3\text{x}$
→
Prove that: $\frac { \tan \left( \frac { \pi } { 4 } + x \right) } { \tan \left( \frac { \pi } { 4 } - x \right) } = \left( \frac { 1 + \tan x } { 1 - \tan x } \right) ^ { 2 }$
→