Class 11MathematicsTrigonometrical Ratios, Functions and IdentitiesMaximum and minimum values of trigonometrical functions, Conditional trigonometrical identities
MediumIf $A+B+C=180^{\circ}$,then the value of $\tan \left(\frac{A}{2}\right) \tan \left(\frac{B}{2}\right)+\tan \left(\frac{B}{2}\right) \tan \left(\frac{C}{2}\right)+\tan \left(\frac{C}{2}\right) \tan \left(\frac{A}{2}\right)$ is
- A$1$
- B$-1$
- C$-2$
- D$2$
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Match 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-$II$ |
| $(I) \ 3 \sin^2 x + 4 \cos^2 x - 2$ | $(a) \ [\frac{1}{4}, 1]$ |
| $(II) \ \cos^2 x + \sin^4 x$ | $(b) \ [-\frac{1}{4}, \frac{1}{4}]$ |
| $(III) \ \sin^6 x + \cos^6 x$ | $(c) \ [1, 2]$ |
| $(IV) \ \cos x \cos(\frac{2 \pi}{3} + x) \cos(\frac{2 \pi}{3} - x)$ | $(d) \ [\frac{3}{4}, 1]$ |
| $(e) \ [0, 1]$ |
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