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# If Cos Theta = 5/13 Find the Value of (Sin^2 Theta - Cos^2 Theta)/(2 Sin Theta Cos Theta) = 3/5 - Mathematics

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#### Question

if cos theta = 5/13 find the value of (sin^2 theta - cos^2 theta)/(2 sin theta cos theta) = 3/5

#### Solution

We have

cos theta == 5/13

In Δ ABC

AC^2 = AB^2 + BC^2

=>(13)^2 = (AB)^2 + (5)^2

=> 169 = (AB)^2 + 25

=> (AB)^2 = 169 - 25

=> AB = 12

:. sin theta = 12/13 and tan theta = 12/5

Now

(sin^2 theta - cos^2 theta) xx  1/tan^2 theta = ((12/13)^2 - (5/13)^2)/(2 xx 12/13 xx 5/13) xx 1/(12/5)^2

= ((144 - 25)/169)/(120/169) xx 25/144

= 119/120 xx 25/144

= (119 xx 5)/(24 xx 144) = 595/3456

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#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 10: Trigonometric Ratios
Ex. 10.1 | Q: 19 | Page no. 25
RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 10: Trigonometric Ratios
Ex. 10.1 | Q: 19 | Page no. 25
Solution If Cos Theta = 5/13 Find the Value of (Sin^2 Theta - Cos^2 Theta)/(2 Sin Theta Cos Theta) = 3/5 Concept: Trigonometric Ratios of an Acute Angle of a Right-angled Triangle.
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