Let A and B denote the statements:A: cos alph | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $\cos (\alpha - \beta) + \cos (\beta - \gamma) + \cos (\gamma - \alpha) = -\frac{3}{2}$.Multiplying by $2$,we get $2[\cos (\alpha - \beta) +

Vedclass · Accepted Answer

both are true

Vedclass · Answer

(B) Given $\cos (\alpha - \beta) + \cos (\beta - \gamma) + \cos (\gamma - \alpha) = -\frac{3}{2}$.Multiplying by $2$,we get $2[\cos (\alpha - \beta) + \cos (\beta - \gamma) + \cos (\gamma - \alpha)] = -3$.Adding $3$ to both sides: $2[\cos (\alpha - \beta) + \cos (\beta - \gamma) + \cos (\gamma - \alpha)] + 3 = 0$.Since $\sin^2 	heta + \cos^2 	heta = 1$,we can write $3 = (\sin^2 \alpha + \cos^2 \alpha) + (\sin^2 \beta + \cos^2 \beta) + (\sin^2 \gamma + \cos^2 \gamma)$.Substituting this into the equation:$(\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma + 2\sin \alpha \sin \beta + 2\sin \beta \sin \gamma + 2\sin \gamma \sin \alpha) + (\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma + 2\cos \alpha \cos \beta + 2\cos \beta \cos \gamma + 2\cos \gamma \cos \alpha) = 0$.This simplifies to $(\sin \alpha + \sin \beta + \sin \gamma)^2 + (\cos \alpha + \cos \beta + \cos \gamma)^2 = 0$.Since the sum of squares is zero,each term must be zero:$\sin \alpha + \sin \beta + \sin \gamma = 0$ and $\cos \alpha + \cos \beta + \cos \gamma = 0$.Therefore,both statements $A$ and $B$ are true.

Let $A$ and $B$ denote the statements:
$A: \cos \alpha + \cos \beta + \cos \gamma = 0$
$B: \sin \alpha + \sin \beta + \sin \gamma = 0$
If $\cos (\alpha - \beta) + \cos (\beta - \gamma) + \cos (\gamma - \alpha) = -\frac{3}{2}$,then:

Similar Questions

If $\sec \theta \cosh y = \operatorname{cosec} x$ and $\operatorname{cosec} \theta \sinh y = \sec x$,then $\sinh ^2 y =$

If $\tan A + \cot A = 4$,then $\tan^4 A + \cot^4 A$ is equal to

If $f(x) = \frac{\cot x}{1 + \cot x}$ and $\alpha + \beta = \frac{5 \pi}{4}$,then the value of $f(\alpha) f(\beta)$ is:

Which of the following statements is/are correct for $0 < \theta < \frac{\pi}{2}$?

If $\alpha = 22^\circ 30'$,then $(1 + \cos \alpha )(1 + \cos 3\alpha )(1 + \cos 5\alpha )(1 + \cos 7\alpha )$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Let $A$ and $B$ denote the statements:$A: \cos \alpha + \cos \beta + \cos \gamma = 0$$B: \sin \alpha + \sin \beta + \sin \gamma = 0$If $\cos (\alpha - \beta) + \cos (\beta - \gamma) + \cos (\gamma - \alpha) = -\frac{3}{2}$,then: