Evaluate- sin 30-tan 45-cosec 60- 30-cos 60- 45-

Sin 30^∘ + tan 45^∘ cosec 60^∘/sec 30^∘ + cos 60^∘ + cot 45^∘ = √(3)+2√(3) 4/2√(3)/4+√(3)+2√(3)/2√(3) = 3√(3) 4/3√(3)+4=3√(3) 4/3√(3)+4×3√(3) 4/3√(3) 4 ...

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Standard X

Mathematics

Range of Trigonometric Ratios from 0 to 90 Degrees

Evaluate: sin...

Question

Evaluate: $\frac{sin 30^{\circ} + tan 45^{\circ} - cosec 60^{\circ}}{sec 30^{\circ} + cos 60^{\circ} + cot 45^{\circ}}$

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Solution

$\frac{sin 30^{\circ} + tan 45^{\circ} - cosec 60^{\circ}}{sec 30^{\circ} + cos 60^{\circ} + cot 45^{\circ}}$

$= \frac{\frac{\sqrt{3} + 2 \sqrt{3} - 4}{2 \sqrt{3}}}{\frac{4 + \sqrt{3} + 2 \sqrt{3}}{2 \sqrt{3}}}$
$= \frac{3 \sqrt{3} - 4}{3 \sqrt{3} + 4}$
$= \frac{3 \sqrt{3} - 4}{3 \sqrt{3} + 4}$ $\times$ $\frac{3 \sqrt{3} - 4}{3 \sqrt{3} - 4}$

$= \frac{27 + 16 - 24 \sqrt{3}}{27 - 16}$
$= \frac{43 - 24 \sqrt{3}}{11}$

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Q. Question 1 (iv)
Evaluate the following:
(iv)

\frac{(s i n 30^{\circ} + t a n 45^{\circ} - c o s e c 60^{\circ})}{(s e c 30^{\circ} + c o s 60^{\circ} + c o t 45^{\circ})}

Solve : $\frac{sin 30^{\circ} + tan 45^{\circ} - c o s e c 60^{\circ}}{sec 30^{\circ} + cos 60^{\circ} + cot 45^{\circ}}$

Evaluate: $\frac{sin 30^{\circ} + tan 45^{\circ} - cosec 60^{\circ}}{cot 45^{\circ} + cos 60^{\circ} - sec 30^{\circ}}$ .

Evaluate : $\frac{s i n 30^{\circ} + t a n 45^{\circ} - c o s e c 60^{\circ}}{s e c 30^{\circ} + c o s 60^{\circ} + c o t 45^{\circ}}$

Evaluate the following

(i) sin60° cos30° + sin30° cos 60°

(ii) 2tan²45° + cos²30° − sin²60°

(iii)

(iv)

(v)

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Evaluate: sin 30∘+tan 45∘−cosec 60∘sec 30∘+cos 60∘+cot 45∘

sin 30∘+tan 45∘−cosec 60∘sec 30∘+cos 60∘+cot 45∘ =√3+2√3−42√34+√3+2√32√3 =3√3−43√3+4=3√3−43√3+4×3√3−43√3−4 =27+16−24√327−16 =43−24√311

Evaluate: $\frac{sin 30^{\circ} + tan 45^{\circ} - cosec 60^{\circ}}{sec 30^{\circ} + cos 60^{\circ} + cot 45^{\circ}}$