Download App

Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions5 Marks
Question
In $\triangle\text{ABC}$ prove that, it $\theta$ be any angle, then $\text{b}\cos\theta=\text{c}\cos(\text{A}-\theta)+\text{a}\cos(\text{C}+\theta).$
✓

Answer

$\text{b}\cos\theta=\text{c}\cos(\text{A}-\theta)+\text{a}\cos(\text{C}+\theta)$
Let $\text{a}\sin\text{C = c}\sin\text{A}$ [Using sine rule]
$\text{RHS}=\text{c}\cos(\text{A}-\theta)+\text{a}\cos(\text{C}+\theta)$
$=\text{c}\cos\text{A}\cos\theta+\text{c}\sin\text{A}\cos\theta+\text{a}\cos\text{C}.\cos\theta-\text{a}\sin\text{C}\sin\theta$
$=\text{k}\sin\text{C}\cos\text{A}\cos\theta+\text{k}\sin\text{C}\sin\text{A}\cos\theta+\text{k}\sin\text{A}\cos\text{C}.\cos\theta\\-\text{k}\sin\text{A}\sin\text{C}\sin\theta$
$=\text{k}\sin\text{C}\cos\text{A}.\cos\theta+\text{k}\sin\text{A}\cos\text{C}.\cos\theta$
$=\text{k}\cos\theta(\sin\text{C}\cos\text{A}+\sin\text{A}\cos\text{C})$
$=\text{k}\cos\theta\sin(\text{C + A})$
$=\text{k}\cos\theta\sin(\pi-\text{B})$
$=\text{k}\cos\theta\sin\text{B}$
$=\text{k}\sin\text{B}.\cos\theta=\text{b}\cos\theta=\text{LHS}$

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 "5 Marks Questions" from Trigonometric Functions→Trigonometric Functions — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}}{\sqrt{1+\text{x}}-\sqrt{1-\text{x}}}$
→
Differentiate the following from first principle

$\sqrt{\tan\text{x}}$

→
Reduce the lines 3x - 4y - 4 = 0 and 2x + 4y - 5 = 0 to the normal form and hence find which line is nearer to the origin.
→
The mean and variance of eight observations are 9 and 9.25 respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.
→
If ${^\text{n+2}}\text{C}_{\text{8}}:{^\text{n-2}}\text{C}_{\text{4}},=57:16,$ Find n.
→
The mid-point of the sides of a triangle are (1, 5, -1), (0, 4, -2) and (2, 3, 4). Find its vertices. Also find the centriod of the triangle.
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\cos\text{ax}-\cos\text{bx}}{\cos\text{cx}-1}$
→

If the 2nd, 3rd and 4th terms in the expansion of $(\text{x}+\text{a})^{\text{n}}$ are 240, 729 and 1080 respectively find x, a, n.

→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\sqrt{1+\text{x}^2}-\sqrt{1+\text{x}}}{\sqrt{1+\text{x}^3}-\sqrt{1+\text{x}}}$
→
Differentiate the following from first principle

$3^{\text{x}^2}$

→