Evaluate - sin 30-tan 45-cosec 60- 300-cos 60- t 55-

Evaluate : sin 30^∘ + tan 45^∘ cosec 60^∘/sec 30^∘ + cos 60^∘ + cot 45^∘ = 1/2 + 1 2/√(3)/2/√(3) + 1/2 + 1 = √(3) + 2√(3) 4 /2√(3)/4 + √(3) + 2√(3)/2√(3) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Trigonometric Identities

Evaluate : si...

Question

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

Open in App

Solution

Evaluate : $\frac{s i n 30^{\circ} + t a n 45^{\circ} - c o s e c 60^{\circ}}{s e c 30^{\circ} + c o s 60^{\circ} + c o t 45^{\circ}}$ = $\frac{\frac{1}{2} + 1 - \frac{2}{\sqrt{3}}}{\frac{2}{\sqrt{3}} + \frac{1}{2} + 1}$

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

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

Suggest Corrections

Similar questions

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

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

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 the following

(i) sin60° cos30° + sin30° cos 60°

(ii) 2tan²45° + cos²30° − sin²60°

(iii)

(iv)

(v)

Join BYJU'S Learning Program

Evaluate : sin30∘+tan45∘−cosec60∘sec30∘+cos60∘+cot45∘

Evaluate : sin30∘+tan45∘−cosec60∘sec30∘+cos60∘+cot45∘ = 12+1−2√32√3+12+1 = √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 : $\frac{s i n 30^{\circ} + t a n 45^{\circ} - c o s e c 60^{\circ}}{s e c 30^{\circ} + c o s 60^{\circ} + c o t 45^{\circ}}$