Q. tan65°/cot25° = ? Q. sin 43° / cos 47° = ?

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Q. tan65°/cot25° = ?

Solⁿ,

65^∘ + 25^∘ = 90^∘ ⇒ complementary

So, cot25^∘ = tan65^∘

Now just replace: tan65^∘/cot25^∘ = tan65^∘/tan65^∘ = 1

So: tan65^∘/^​ cot25^∘ = tan65^∘/tan65^∘ ​=1

Ans:1​

Final Key Trick

If angles add to 90° and appear as:

• sin / cos


• tan / cot


• sec / cosec

then value = 1

Q. sin 43° / cos 47° = ?

Solⁿ,
43° + 47° = 90° ⇒ complementary  and cos (90° - θ) = sin θ

So,

cos 47° = cos (90° – 43°) = sin 43°

Now substitute: sin43°/cos47° = sin43°/sin43°= 1

Ans: 1

Simple

Q1. sin 35° / cos 55° = ?

Solⁿ

Check: 35° + 55° = 90° (Complementary)

cos 55° = sin (90° – 55°) = sin 35°

sin35°/cos55°

= sin35°/sin35°

=1

Ans = 1

Q2. tan 28° / cot 62° = ?

Solⁿ

Check: 28° + 62° = 90°

cot 62° = tan (90° – 62°) = tan 28°

tan28°/cot 62°

= tan28°

= 1

Ans = 1

B. Medium

Q3. cos 18° / sin 72° = ?

Solⁿ

Check: 18° + 72° = 90°

sin 72° = cos (90° – 72°) = cos 18°

cos18°/sin72°

= cos18°/ cos18°  ​

= 1 (sin72° replace value cos18°)

Ans = 1

Q4. sec 41° / cosec 49° = ?

Solⁿ

Check: 41° + 49° = 90°

cosec 49° = sec (90° – 49°) = sec 41°

sec41°/cosec49°

= sec41°/sec41°

= 1, (cosec49° replace value sec41°)

Ans = 1

Tough

Q5. (sin 22° × tan 68°) / (cos 68° × cot 22°) = ?

Solⁿ

Break using complementary:

• tan 68° = cot 22°


• cos 68° = sin 22°

sin22° × tan68°/ cos68°× cot22°

= sin22°× cot22°/sin22°× cot22°

= 1 (tan68° / cos68° replace value cot22°/sin22°)

Ans = 1

Q6. (sec 33° × sin 57°) / (cosec 33° × cos 57°)

Solⁿ

Check complementary:

• 33° + 57° = 90°


• sin 57° = cos 33°


• cos 57° = sin 33°

Now:

Numerator: sec33°⋅ sin57°= 1/cos33° * cos33° = 1

Denominator: cosec33°⋅ cos57°= 1/sin33°⋅ sin33°=1

1/1=1

Ans = 1

Final Key Trick

If angles add to 90° and appear as:

• sin / cos


• tan / cot


• sec / cosec

then value = 1