Download App

Sine And Cosine Formulae And Their Applications — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsSine And Cosine Formulae And Their Applications3 Marks
Question
$\text{b}\cos\text{B + c}\cos\text{C}=\text{a}\cos(\text{B}-\text{C})$
✓

Answer

$\text{b}\cos\text{B + c}\cos\text{C}=\text{a}\cos(\text{B}-\text{C})$
Let $\text{a = k}\sin\text{A,b = k}\sin\text{B,c = k}\sin\text{C}$
$\text{LHS}=\text{b}\cos\text{B + c}\cos\text{C}$
$=\text{k}\sin\text{B}\cos\text{B}+\text{k}\sin\text{C}\cos\text{C}$
$=\frac{\text{k}}{2}(2\sin\text{B}\cos\text{B}+2\sin\text{C}\cos\text{C})$
$=\frac{\text{k}}{2}(\sin2\text{B}+\sin2\text{C})$
$=\frac{\text{k}}{2}2\sin(\text{B + C})\cos(\text{B}-\text{C})$
$=\text{k}\sin(\pi-\text{A})\cos(\text{B}-\text{C})$
$=\text{k}\sin\text{A}\cos(\text{B}-\text{C})$
$=\text{a}\cos(\text{B}-\text{C})=\text{RHS}$

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 "Solve the Following Question.(3 Marks)" from Sine And Cosine Formulae And Their Applications→Sine And Cosine Formulae And Their Applications — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the equation of the parabola whose focus is $(5, 2)$ and having vertex at $( 3, 2)$.
→
Let $A$ and $B$ be independent events with $P(A)=\frac{1}{4}$ and $P(A \cup B)=2 P(B)-P(A)$. Find

(i) P(B)

2. P(A/B)

3. P(B’/A)

→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow3}\big(\text{x}^2-9\big)\Big(\frac{1}{\text{x}+3}-\frac{1}{\text{x}-3}\Big)$
→
Find the domain of the following real valued functions of real variable:
$\text{f(x)}=\frac{1}{\text{x}}$
→
Find the derivatives of the following w.r.t. x by using the method of the first principle.

tan(2x + 3)

→
The probability that a person will travel by plane is $\frac{3}{5}$ and that he will travel by trains is $\frac{1}{4}.$ What is the probability that he (she) will travel by plane or train?
→
Find the equation of a circle with a radius of 4 units and touch both the co-ordinate axes having centre in the third quadrant.
→
Find the equation of the hyperbola referred to its principal axes: whose length of transverse axis is $8$ and distance between foci is $10.$
→
Prove that: $\Big(2^{\frac14}.4^{\frac18}.8^{\frac{1}{16}}.16^{\frac{1}{32}}\dots\infty\Big)=2$
→
If $x=\log _a b c, y=\log _b c a, z=\log _c a b$, then prove that $\frac{1}{1+x}+\frac{1}{1+y}+\frac{1}{1+z}=1$.
→