Question

cos square(45+theta)+cossqaure(45-theta) / tan(60+theta) × tan(30-theta)+ cot30+sin90×tan60-sec0​

Answer 1

Solution

→ [cos²(45 + ∅) + cos²(45 - ∅)]/[tan(60 + ∅) tan(30 - ∅) + cot30 + sin90 tan60 - sec0]

→ [sin²(90 - 45 - ∅) + cos²(45 - ∅)]/[cot(90 - 60 - ∅) tan(30 - ∅) + √3 + 1 × √3 - 1]

→ [sin²(45 - ∅) + cos²(45 - ∅)]/[cot(30 - ∅) tan(30 - ∅) + √3 + √3 - 1]

→ 1/(1 + √3 + √3 - 1)

→ 1/2√3 or √3/6 [Rationalized]

Remember

• sin(90 - ∅) = cos∅
• cot 30° = tan 60° = √3
• sec 0° = 1/cos 0° = 1
• cot∅ × tan∅ = 1
• sin²∅ + cos²∅ = 1