Question

Without using the trigonometric tables, find the values of :
i) sin 45° cos 30° - cos 45° sin 30°​

Answer 1

Sin 45°=1/√2

Cos45°=1/√2

sin30°=1/2

Cos30°=√3/2

Therefore

=Sin45°×cos30°+cos45°×sin30°

=1\√2 × √3\2 + 1\√2 × 1\2

=√3\2√2 + 1\2√2

=√3 +1\2√2

Therefore answer is √3+1\2√2

Hope it's helpful to you

Answer 2

Answer:

Sin 45°=1/√2

Sin 45°=1/√2Cos45°=1/√2

Sin 45°=1/√2Cos45°=1/√2sin30°=1/2

Sin 45°=1/√2Cos45°=1/√2sin30°=1/2Cos30°=√3/2

Sin 45°=1/√2Cos45°=1/√2sin30°=1/2Cos30°=√3/2Therefore

Sin 45°=1/√2Cos45°=1/√2sin30°=1/2Cos30°=√3/2Therefore=Sin45°×cos30°+cos45°×sin30°

Sin 45°=1/√2Cos45°=1/√2sin30°=1/2Cos30°=√3/2Therefore=Sin45°×cos30°+cos45°×sin30°=1\√2 × √3\2 + 1\√2 × 1\2

Sin 45°=1/√2Cos45°=1/√2sin30°=1/2Cos30°=√3/2Therefore=Sin45°×cos30°+cos45°×sin30°=1\√2 × √3\2 + 1\√2 × 1\2=√3\2√2 + 1\2√2

Sin 45°=1/√2Cos45°=1/√2sin30°=1/2Cos30°=√3/2Therefore=Sin45°×cos30°+cos45°×sin30°=1\√2 × √3\2 + 1\√2 × 1\2=√3\2√2 + 1\2√2=√3 +1\2√2

Sin 45°=1/√2Cos45°=1/√2sin30°=1/2Cos30°=√3/2Therefore=Sin45°×cos30°+cos45°×sin30°=1\√2 × √3\2 + 1\√2 × 1\2=√3\2√2 + 1\2√2=√3 +1\2√2Therefore answer is √3+1\2√2