Download App

Trigonometric Ratios Of Compounds — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compounds3 Marks
Question
Prove that: $\cos4\text{x}-\cos4\alpha=8(\cos\text{x}-\cos\alpha)(\cos\text{x}+\cos\alpha)\$\cos\text{x}+\sin\alpha)(\cos\text{x}-\sin\alpha)$
✓

Answer

$\cos4\text{x}-\cos4\alpha=2\cos^22\theta-2\cos^22\alpha$ $=2(\cos2\text{x}+\cos2\alpha)(\cos2\text{x}-\cos2\alpha)$ $=2(2\cos^2\text{x}-1+1-2\sin^2\alpha)(2\cos^2\text{x}-1-2\cos^2\alpha+1)$ $=8(\cos^2\text{x}-\sin^2\alpha)(\cos^2\text{x}-\cos^2\alpha)$ $=8(\cos\text{x}-\sin\alpha)(\cos\text{x}+\sin\alpha)(\cos\text{x}-\cos\alpha)$

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

If P and Q are two sets such that P has 40 elements, $\text{P}\cup\text{Q}$ has 60 elements and $\text{P}\cap\text{Q}$ has 10 elements, how many elements does Q have?
→
Find the domain and range of the following real valued functions: f(x) = -|x|
→
Find the number of diagonals of:
  1. A hexagon.
  2. A polygon of 16 sides.
→
Find the equation of the line passing through the intersection of the lines 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
→
Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b $ \in $A, b is exactly divisible by a}.
  1. Write R in roster form
  2. Find the domain of R
  3. Find the range of R.
→
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?
→
Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to a line having slope $\frac{3}{4}.$
→
Find the number of diagonals of:
  1. A hexagon.
  2. A polygon of 16 sides.
→
Find the distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of x + 2y = 5 and x - 3y = 7.
→
Evaluate the following one sided limits: $\lim\limits_{\text{x}\rightarrow0^-}\frac{\text{x}^2-3\text{x}+2}{\text{x}^3-2\text{x}^2}$
→