Question

evaluate : (sin 37°/cos53°)+(2 tan42°/cot48°)-(sin54°/cosec 36°)

show the steps
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Answer 1

I have written it by myself please mark it as the brainllist if it will help you

Answer 2

$\displaystyle \sf{ \frac{sin \: {37}^{ \circ} }{cos \: {53}^{ \circ} } + \frac{2 \: tan \: {42}^{ \circ} }{cot \: {48}^{ \circ} } - \frac{sec \: {54}^{ \circ} }{cosec \: {36}^{ \circ} } } = 2$

Given :

$\displaystyle \sf{ \frac{sin \: {37}^{ \circ} }{cos \: {53}^{ \circ} } + \frac{2 \: tan \: {42}^{ \circ} }{cot \: {48}^{ \circ} } - \frac{sec \: {54}^{ \circ} }{cosec \: {36}^{ \circ} } }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ \frac{sin \: {37}^{ \circ} }{cos \: {53}^{ \circ} } + \frac{2 \: tan \: {42}^{ \circ} }{cot \: {48}^{ \circ} } - \frac{sec \: {54}^{ \circ} }{cosec \: {36}^{ \circ} } }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ \frac{sin \: {37}^{ \circ} }{cos \: {53}^{ \circ} } + \frac{2 \: tan \: {42}^{ \circ} }{cot \: {48}^{ \circ} } - \frac{sec \: {54}^{ \circ} }{cosec \: {36}^{ \circ} } }$

$\displaystyle \sf{ = \frac{sin \: ( {90}^{ \circ} -{53}^{ \circ}) }{cos \: {53}^{ \circ} } + \frac{2 \: tan \:( {90}^{ \circ} - {48}^{ \circ})}{cot \: {48}^{ \circ} } - \frac{sec \: ({90}^{ \circ} - {36}^{ \circ} ) }{cosec \: {36}^{ \circ} } }$

$\displaystyle \sf{ = \frac{cos \: {53}^{ \circ} }{cos \: {53}^{ \circ} } + \frac{2 \: cot \: {48}^{ \circ}}{cot \: {48}^{ \circ} } - \frac{cosec \: {36}^{ \circ} }{cosec \: {36}^{ \circ} } }$

$\displaystyle \sf{ =1 + 2 - 1 }$

$\displaystyle \sf{ =2 }$

Correct question : evaluate : (sin 37°/cos 53°) + (2 tan 42°/cot 48°) - (sec 54°/cosec 36°)

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