Download App

Trigonometric Ratios Of Compound Angles — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Ratios Of Compound Angles1 Mark
Question
If $\tan\frac{\text{x}}{2}=\frac{\text{m}}{\text{n}},$ then write the value of $\text{m}\ \sin\text{x}+\text{n}\cos\text{x}.$
✓

Answer

We have,
$\tan\frac{\text{x}}{2}=\frac{\text{m}}{\text{n}}$
$\Rightarrow\frac{\sin\frac{\text{x}}{2}}{\cos\frac{\text{x}}{2}}=\frac{\text{m}}{\text{n}}$
$\Rightarrow\sin\frac{\text{x}}{2}=\text{mk},\&\cos\frac{\text{x}}{2}=\text{nk}(\text{say})$
Now,
$\text{m}\sin\text{x}+\text{n}\cos\text{x}$
$=\text{m}2\sin\frac{\text{x}}{2},\cos\frac{\text{x}}{2}+\text{n}\Big(\cos^2\frac{\text{x}}{2}-\sin^2\frac{\text{x}}{2}\Big)$
$2\text{m}.\text{mk}.\text{nk}+\text{n}(\text{n}^2\text{k}^2-\text{m}^2\text{k}^2)$
$=2\text{m}^2\text{k}^2\text{n}+\text{nk}^2(\text{n}^2-\text{m}^2)$
$=\text{nk}^2(2\text{m}^2+\text{n}^2-\text{m}^2)$
$=\text{nk}^2(\text{m}^2+\text{n}^2)$
$=​​\text{n}(​\text{m}^2​\text{k}^2+​\text{n}^2​\text{k}^2)$
$​\text{n}=\Big(\sin^2\frac{​\text{x}}{2}+\cos^2\frac{​\text{x}}{2}\Big)$
$=​\text{n}$

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 "1 Marks Question" from Trigonometric Ratios Of Compound Angles→Trigonometric Ratios Of Compound Angles — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Write down the negation of following compound statement:
|x| is equal to either x or -x.
→
Consider the sets $\phi$, A = { 1, 3 }, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}. Insert the symbol $⊂ or ⊄$ between the pair of sets: B . . . C
→
Identify the Quantifiers in the following statement:
For all real numbers $x$ with $x > 3, x^2$ is greater than $9$.
→
Check whether the following statement are true or not:
q: If x, y are integers such that xy is even, then at least one of x and y is an even integer.
→
Write down the converse of following statement:
If S is a cyclic quadrilateral, then the opposite angles of S are supplementary.
→
If the sum of $n$ terms of an $A.P.$ is $2n^2 + 5 n,$ then its $n^{th}$ term is
→
Write the negation of the following statements:
r: There exists a number x such that 0 < x < 1.
→
Check the validity of the following statements:
p: 100 is a multiple of 4 and 5.
→
Find the derivative of function $\frac{x}{{1 + \tan x}}$ (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers).
→
Find the derivative of $f(x) = 1 + x + x^2 + x^3 + ... + x^{50} $ at $x = 1.$
→