Question

Evaluate:
cos 37 cosec 53/
tan 5 fan 25 tan 45 tan65 tan 85

pls help...its urgent​

Answer 1

Answer:

1

Step-by-step explanation:

cos 37 cosec 53 / tan 5 tan25 tan45 tan65 tan85

= cos37*sec37 / tan5*tan25*tan45*cot25*cot5

= 1/1

= 1

Answer 2

$\frac{\cos(37^{ \circ} ) \csc(53^{ \circ})}{ \tan(5^{ \circ}) \tan(25^{ \circ}) \tan(45^{ \circ}) \tan(65^{ \circ}) \tan(85^{ \circ}) } = \bf 1$

Given:

• $\frac{\cos(37^{ \circ} ) \csc(53^{ \circ})}{ \tan(5^{ \circ}) \tan(25^{ \circ}) \tan(45^{ \circ}) \tan(65^{ \circ}) \tan(85^{ \circ}) }$

To find:

• Find the value of trigonometric expression.

Solution:

Formula to be used:

1. $\csc(90^{ \circ}- \theta) = sec \: \theta$
2. $tan(90^{ \circ}- \theta) = cot \: \theta$
3. $tan \: {45}^{ \circ} = 1$
4. $tan \: \theta \times cot \: \theta = 1$
5. $cos \: \theta \times sec \: \theta = 1$

Step 1:

Apply complementary angle formulas 1 and 2 as discussed above.

$\frac{\cos(37^{ \circ} ) \csc(90^{ \circ} - 37^{ \circ})}{ \tan(90^{ \circ} - 85^{ \circ}) \tan(90^{ \circ} -65 ^{ \circ}) \tan(45^{ \circ}) \tan(65^{ \circ}) \tan(85^{ \circ}) }$

or

$\frac{\cos(37^{ \circ} ) \sec(37^{ \circ}) }{ \cot(85^{ \circ}) \cot(65^{ \circ}) \tan(45^{ \circ}) \tan(65^{ \circ}) \tan(85^{ \circ}) }$

Step 2:

Apply trigonometric identities 3,4, and 5.

$\frac{\cos(37^{ \circ} ) \sec(37^{ \circ}) }{ \cot(85^{ \circ})\tan(85^{ \circ}) \cot(65^{ \circ}) \tan(65^{ \circ}) \tan(45^{ \circ}) }$

or

$= \frac{1}{1 \times 1 \times 1}$

or

$\frac{\cos(37^{ \circ} ) \csc(53^{ \circ})}{ \tan(5^{ \circ}) \tan(25^{ \circ}) \tan(45^{ \circ}) \tan(65^{ \circ}) \tan(85^{ \circ}) } = 1$

Thus,

Value of given trigonometric equation is 1.

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