Question

evaluate :- sin30degree+tan45degree - cosec60degree upon sec30degree + cos60degree +cot45dregree

Answer 1

To Evaluate

→ (sin30° + tan45° - cosec60°)/(sec30° + cos60° + cot45°)

Evaluation

First we will crack the numerator,

→ sin30° + tan45° - cosec60°

• sin30° = ½
• tan45° = 1
• cosec60° = 2/√3

→ 1/2 + 1 - 2/√3

→ 1/2 + 1 - 2√3/3

→ (3 + 6 - 4√3)/6

→ (9 - 4√3)/6

Now on solving denominator,

→ sec30° + cos60° + cot45°

• sec30° = 2/√3
• cos60° = 1/2
• cot45° = 1

→ 2/√3 + 1/2 + 1

→ (9 + 4√3)/6

→ A/q = (9 - 4√3)/6 × 6/(9 + 4√3)

→ (9 - 4√3)/(9 + 4√3)

On rationalizing we get,

→ (9 - 4√3)²/(81 - 48)

→ (81 + 48 - 72√3)/33

→ (129 - 72√3)/33

Hence evaluated form is (129 - 72√3)/33.