Question

If sin 30° + cos 45° = X, then the value of X.

A) (2√2-√3)/2 B) 4/√3 C) (1-√3)/√3 D) (1+√2)/2

Answer 1

Given :

• sin30° + cos45° = X

To find :

• Value of X.

Solution :

sin30° + cos45° = X

→ 1/2 + 1/√2 = X

→( √2 + 2 )/ 2√2 = X

→ (√2+2)2√2 / 2√2 × 2√2 = X

→ (4+4√2)/8 = X

→ 4(1+√2)/8 = X

→ (1+√2)/2 = X

Therefore, option (D) (1+√2)/2 is correct.

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Some values :-

• sin30° = 1/2
• sin45° = 1/√2
• sin60° = √3/2
• cos30° = √3/2
• cos45° = 1/√2
• cos60° = 1/2
• tan30° = 1/√3
• tan45° = 1
• tan60° = √3

Some formulas :-

★ sin²A + cos²A = 1

★ 1 + tan²A = sec²A

★ 1 + cot²A = cosec²A

★ cos²A - sin²A = cos2A