Q. (sin31°/cos59°)^2 + (cos29°/sin61°)^2 – 1 = ?

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 Q. (sin31°/cos59°)² + (cos29°/sin61°)² – 1 = ?

Solⁿ,

Use complementary angles : 31° + 59° = 90° → Sin 31° = Cos 59°

Sin31°/ Cos 59°​ = 1

So, (Sin31° / Cos 59°)² = 1

29° + 61° = 90° → Cos 29° = Sin 61°

Cos29°​/Sin 61° = 1

So, (Cos29°​/Sin 61°)²=1

Substitute: 1+1−1=1

Ans:1​

Note: α + β = 90° , sin α /cos β = 1, tan α /cot β = 1, sec α /cosec β = 1

Final Key Trick

If angles add to 90° and appear as:

• sin / cos


• tan / cot


• sec / cosec

then value = 1

α