Question

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Ch - Trigonometry...

Plz make sure that ur answer is 595/3456

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Answer 1

Answer:

answer for the given problem is given

Answer 2

Question

If sin theta = 12/13

Find : Sin²theta – Cos²theta / 2Sin theta . Cos theta × 1/tan²theta

Solution

Given : sin theta = 12/13

Cosider a right angled triangle

In which Perpendicular= 12 , Hypotenuse = 13 and base =?

Now by using Pythagoras theorem find base

Base² = Hypotenuse ²- Perpendicular ²

Base² = 13² - 12²

$base \: = \sqrt{169 - 144}$

$base = \sqrt{25}$

base = 5

Then Sin theta = p/h

= 12/13,

Cos theta = b/h

= 5/13,

and tan theta = p/b

= 12/5

Now put the value

A/q

$\frac{sin {}^{2} \: - cos {}^{2} }{2 sin.cos} \times \frac{1}{tan {}^{2} }$

$= > \frac{ (\frac{12 }{13}) {}^{2} - (\frac{5 }{13} ) {}^{2} }{ \frac{2 \times 12}{13} \times \frac{5}{13} } \times \frac{1}{ (\frac{12 }{5}) {}^{2} }$

$= > \frac{ \frac{144}{169} - \frac{25}{169} }{ \frac{24}{13} \times \frac{5}{13} } \times \frac{1}{ \frac{144}{25} }$

$= > \frac{ \frac{119}{169} }{\frac{120}{169} } \times \frac{25}{144}$

$= > ( \frac{119}{169} \times \frac{169}{120}) \times \frac{25}{144}$

$= > \frac{119}{120} \times \frac{25}{144}$

$= > \frac{119}{24} \times \frac{5}{144}$

$= > \frac{595}{3456}$

Therefore, answer is 595/3456

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