Question

Evaluate :


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


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Answer 1

HELLO FRIEND!!!!!!

question 1:

$\frac{ \tan(36) }{ \cot(54) }$

we know the identity that :

$\tan(90 - theeta) = \cot(theeta)$

thus,

$\tan(36) = \tan(90 - 36)$

$\tan(36) = \cot(54)$

thus equation becomes:

$\frac{ \cot(54) }{ \cot(54) }$

$1$

thus answer of question 1 is 1

question 2

$\cos(12) - \sin(78)$

again using same identity,

where theeta is 12 degree....

$\cos(12) = \sin(90 - 12)$

$\cos(12) = \sin(78)$

so equation becomes...

$\sin(78) - \sin(78)$

which is 0.....

thus answer of question 2 becomes 0

question 3

$\csc(31) - \sec(58)$

using same identity ...

$\csc(31) = \csc(90 - 59)$

so here there is an error in question...the question should be sec 59 degree .....

$\sec(58)$

$- \sec(58)$

which is 0

thus answer of corrected question 3 would be 0 ..

THANK YOU