Download App

Trigonometric Ratios Of Compounds — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compounds2 Marks
Question
If $\text{a}\cos2\text{x}+\text{b}\sin2\text{x}=\text{c}$ has $\alpha$ and $\beta$ as its roots, then prove that, $\tan(\alpha+\beta)=\frac{\text{b}}{\text{a}}$
✓

Answer

$\cos2\theta=\frac{1-\tan^2\theta}{1+\tan^2\theta}$ $\sin^2\theta=\frac{2\tan\theta}{1+\tan^2\theta}$ substitute these valuse in the given equation, it reduces to $\text{a}(1-\tan^2)+\text{b}(2\tan\theta)=\text{c}(1+\tan^2\theta)$ $(\text{c+a})\tan^2\theta+2\text{b}\tan\theta+\text{C-a}=0$ As $\alpha$ and $\beta$ are roots $\tan(\alpha+\beta)=\frac{\tan\alpha+\tan\beta}{1-\tan\alpha\tan\beta}=\frac{2\text{b}}{\text{c+a=c+a}}=\frac{\text{b}}{\text{a}}$

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 2 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

Solve the following system of equations in R. $11-5\text{x}>-4, \ 4\text{x}+13\leq-11$
→
A card is drawn at random from a pack of 52 cards, find the probability that the card drawn is:Spade or an ace.
→
Express the following complex numbers in the standard form a + ib: $\frac{1-\text{i}}{1+\text{i}}$
→
If the function f(x) satisfies $\mathop {\lim }\limits_{x \to 1} \frac{{f(x) - 2}}{{{x^2} - 1}} = \pi ,$ then evaluate $\mathop {\lim }\limits_{x \to 1} f(x)$.
→
Prove that : (sin 3x + sin x) sin x + (cos 3x - cos x) cos x = 0
→
Classify the following pairs of lines as coincident, parallel or intersecting: 2x + y - 1 = 0 and 3x + 2y + 5 = 0
→
A die is thrown twice Each time the number appearing on it is recorded Describe the following events: C = sum of the numbers is less than Also, find A ∪ B, A ∩ B, A ∪ C, A ∩ C Which pairs of events are mutually exclusive?
→
Find the value of tan $15^o$
→
Solve ${x^2} + \frac{x}{{\sqrt 2 }} + 1 = 0$
→
Find the derivative of $1/x^2$ from the first principle.
→