Q. tan65┬░/cot25┬░┬а= ?

Q. tan 65° / cot 25° = ?


Soln:
65° + 25° = 90° ⇒ complementary angles


So, cot 25° = tan 65°


Now replace: tan 65° / cot 25° = tan 65° / tan 65° = 1


Ans: 1


рдкреНрд░рд╢реНрди: tan 65° / cot 25° = ?


рд╕рдорд╛рдзрд╛рди:
65° + 25° = 90° ⇒ рдкреВрд░рдХ рдХреЛрдг


рдЕрддрдГ, cot 25° = tan 65°


рдЕрдм рдХреЗрд╡рд▓ рдорд╛рди рд░рдЦреЛ: tan 65° / cot 25° = tan 65° / tan 65° = 1


рдЙрддреНрддрд░: 1


ржкрзНрз░рж╢рзНржи: tan 65° / cot 25° = ?


рж╕ржорж╛ржзрж╛ржи:
65° + 25° = 90° ⇒ рж╕ржорзНржкрзВрз░ржХ ржХрзЛржг


рж╕рзЗржпрж╝рзЗ, cot 25° = tan 65°


ржПрждрж┐ржпрж╝рж╛ ржорж╛ржерзЛржБ ржорж╛ржиржЯрзЛ ржмрж╕рж╛ржУ: tan 65° / cot 25° = tan 65° / tan 65° = 1


ржЙрждрзНрждрз░: 1


 



Key Trick


If angles add to 90° / рдпрджрд┐ рдХреЛрдгреЛрдВ рдХрд╛ рдпреЛрдЧ 90° рд╣реЛ / ржпржжрж┐ ржХрзЛржгрж╕ржорзВрж╣рз░ ржпрзЛржЧржлрж▓ 90° рж╣ржпрж╝
and appear as / рдФрд░ рдЗрд╕ рд░реВрдк рдореЗрдВ рд╣реЛрдВ / ржЖрз░рзБ ржПржЗ ржзрз░ржгрзЗ ржерж╛ржХрзЗ:



  • sin / cos

  • tan / cot

  • sec / cosec


then value = 1 / рддреЛ рдорд╛рди = 1 / рждрзЗржирзНрждрзЗ ржорж╛ржи = 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°  тАЛ


= 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