Class 11MathematicsTrigonometrical Ratios, Functions and IdentitiesMaximum and minimum values of trigonometrical functions, Conditional trigonometrical identities
EasyIf $A + B + C = 270^o,$ then $\cos 2A + \cos 2B + \cos 2C + 4\sin A \sin B \sin C = $
- A$0$
- B$1$
- C$2$
- D$3$
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Similar Questions
If $A + B + C = 180^{\circ}$,then $\tan A + \tan B + \tan C = $
Difficult
View SolutionMatch the ranges of the functions given in List-$I$ with those of the items given in List-$II$:
List-$I$ List-$II$ $(I) \ 3 \sin^2 x + 4 \cos^2 x - 2$ $(a) \ [\frac{1}{4}, 1]$ $(II) \ \cos^2 x + \sin^4 x$ $(b) \ [-\frac{1}{4}, \frac{1}{4}]$ $(III) \ \sin^6 x + \cos^6 x$ $(c) \ [1, 2]$ $(IV) \ \cos x \cos(\frac{2 \pi}{3} + x) \cos(\frac{2 \pi}{3} - x)$ $(d) \ [\frac{3}{4}, 1]$ $(e) \ [0, 1]$
| List-$I$ | List-$II$ |
| $(I) \ 3 \sin^2 x + 4 \cos^2 x - 2$ | $(a) \ [\frac{1}{4}, 1]$ |
| $(II) \ \cos^2 x + \sin^4 x$ | $(b) \ [-\frac{1}{4}, \frac{1}{4}]$ |
| $(III) \ \sin^6 x + \cos^6 x$ | $(c) \ [1, 2]$ |
| $(IV) \ \cos x \cos(\frac{2 \pi}{3} + x) \cos(\frac{2 \pi}{3} - x)$ | $(d) \ [\frac{3}{4}, 1]$ |
| $(e) \ [0, 1]$ |
The smallest value of $5 \cos \theta + 12$ is
If $\alpha+\beta+\gamma=2 \theta$,then $\cos \theta+\cos (\theta-\alpha)+\cos (\theta-\beta)+\cos (\theta-\gamma)$ is equal to
If $A+B=C$,then the value of $\cos ^2 A+\cos ^2 B+\cos ^2 C-2 \cos A \cos B \cos C$ is equal to:
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