If tan 2 45-cos 2 30-x sin 45-cos 45- then x-a 2b -2c -12d 12

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Relation between Trigonometric Ratios

If tan 2 45∘-...

Question

If tan² 45° − cos² 30° = x sin 45° cos 45°, then x =

(a) 2
(b) −2
(c) $- \frac{1}{2}$
(d) $\frac{1}{2}$

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Solution

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\frac{1}{2}

- \frac{1}{2}

{tan}^{2} 45^{\circ} - {cos}^{2} 30^{\circ} = x sin 45^{\circ} cos 45^{\circ}

{tan}^{2} 45^{\circ} - {cos}^{2} 30^{\circ} = x sin 45^{\circ} cos 45^{\circ}

x =

x sin 45^{\circ} cos 45^{\circ} + {tan}^{2} 60^{\circ} = {sec}^{2} 30^{\circ} c o s e c^{2} 30^{\circ}

Evaluate the following

(i) sin60° cos30° + sin30° cos 60°

(ii) 2tan²45° + cos²30° − sin²60°

(iii)

(iv)

(v)

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