Download App

Trigonometric Ratios Of Compounds — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compounds3 Marks
Question
Prove that: $\cos7^\circ\cos14^\circ\cos28^\circ\cos56^\circ=\frac{\sin68^\circ}{16\cos83^\circ}$
✓

Answer

$\text{LHS}=\cos7^\circ\cos14^\circ\cos28^\circ\cos56^\circ$ Divide and miltiply by $2\sin7^\circ,$ weget $\frac{1}{2\sin7^\circ}.2\sin7^\circ.\cos14^\circ.\cos28^\circ.\cos56^\circ$ $=\frac{2\sin14^\circ}{2.2\sin7^\circ}.2\cos14^\circ.\cos28^\circ.\cos56^\circ$ $=\frac{2\sin28^\circ}{2.4\sin7^\circ}.\cos28^\circ.\cos56^\circ$ $=\frac{2\sin56^\circ}{2.8\sin7^\circ}.\cos56^\circ$ $=\frac{\sin112^\circ}{16\sin7^\circ}$ $=\frac{\sin(180^\circ-68^\circ)}{16\sin(90^\circ-83^\circ)}$ $=\frac{\sin68^\circ}{16\cos83^\circ}=\text{RHS}$

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 "(Each question 3 marks)" from Trigonometric Ratios Of Compounds→Trigonometric Ratios Of Compounds — 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 sum of the following series: 7 + 77 + 77 + ... to n terms.
→
From a well shuffled deck of 52 cards, 4 cards are drawn at random. What is the probability that all the drawn cards are of the same colour.
→
If ${^\text{n}}\text{C}_{12}={^\text{n}}\text{C}_{5},$ Find the value of n.
→
If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first $(p + q)$ terms.
→
The ratio of the sum of $m$ and $n$ terms of an A.P. is $m^2: n^2$ Show that the ratio of $m^{\text {th }}$ and $n^{\text {th }}$ term is $(2 m-1):(2 n-1)$.
→
Let $f: R \rightarrow R$ and $g: C \rightarrow C$ be two functions defined as $f(x)=x^2$ and $g(x)=x^2$. Are they equal functions?
→
Find the equation of the ellipse, whose length of the major axis is $20$ and foci are (0, $\pm$ 5).
→
Which term of the G.P.:$\frac13,\frac19,\frac{1}{17}\ ...\text{is}\frac{1}{19683}?$
→
If $\frac{\text{z}-1}{\text{z}+1}$ is purely imaginary number $(\text{z}\neq-1),$ find the value of $|\text{z}|.$
→
Evaluate:$\sum \limits_ { k = 1 } ^ { 11 } \left( 2 + 3 ^ { k } \right)$
→