Question

Evaluate :

i) tan 36°/cot 54°
ii) cos 12° - sin 78°
iii) cosec 31° - sec 58°
​

Answer 1

i) tan36°/cot54°

=tan(90°-54°)/cot 54°

=cot54°/cot54°

=1

ii) cos12°- sin78°

=cos(90°-78°) - sin78°

=sin78°- sin78°

=0

iii) cosec 31° - sec 58°

=cosec 31° - sec (90° - 31°)

=cosec 31° - cosec 31°

=0

$<marquee>Hope it helps you,</marquee>$

$<marquee>Please mark me as brainlist and follow me.</marquee>$

Answer 2

☺ $\rm\bold\orange{To\:Kaise\:Hai\:Aap\:Log}$✌

$\rule{200}{4}$

$\huge\bold\purple{♡\:} {\orange{\underline{\red{\mathbf{ Question}}}}} \bold\purple{\:♡}$

Evaluate :

i) tan 36°/cot 54°

ii) cos 12° - sin 78°

iii) cosec 31° - sec 58°

$\huge\bold\purple{♡\:} {\orange{\underline{\pink{\mathbf{ Solution}}}}} \bold\purple{\:♡}$

i) Given that : tan 36°/cot 54°

➟ tan 36°/cot (90° - 36°)

➟ [∵ cot (90 - ⊖) = tan ⊖]

➟ tan 36°/tan 36° = 1

ii) Given that : cos 12° - sin 78°

➟ cos 12° - sin (90° - 12°)

➟ [∵ sin (90 - ⊖) = cos ⊖]

➟ cos 12° - cos 12° = 0

iii) Given that : cosec 31° - sec 59°

➟ cosec 31° - sec (90° - 31°)

➟ [∵ sec (90 - ⊖) = cosec ⊖]

➟ cosec 31° - cosec 31° = 0

$\rule{200}{4}$