1.

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Solution

Given :-

  • SIN θ = 12/13 -------------equ(1)

Find:-

  • VALUE of (sin² θ - cos² θ)/(2sinθ cosθ) × (1/tan²θ)

Explanation

We know,

★ sin θ = (PERPENDICULAR)/(Hypotenuse)

★ cos θ = Base/Hypotenuse

★ tan θ = perpendicular/BASE

Here,

  • sin θ = (Perpendicular)/(Hypotenuse) = 12/13

So, First we calculate Base

By, Pythagoras Theorem

★ (Perpendicular)² + (Base)² = (Hypotenuse)²

So,

==> Base ² = (Hypotenuse)² - (Perpendicular)²

==> Base = √[(13)²-(12)²]

==> Base = √[169-144]

==> Base = √25

==> Base = 5

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Now, Calculate cos θ & tan θ

★ tan θ = perpendicular/Base = 12/5

★ cos θ = Base/Hypotenuse = 5/13

So, calculate (sin² θ - cos² θ)/(2sinθ cosθ) × (1/tan²θ)

Keep all above values

= {(12/13)² - (5/13)²}/{2*(12/13)*(5/13)} × {1/(12/5)²}

= { (144/169 - 25/169 )/(120/169)} × ( 25/144)

= {(144-25)/169} × 169/120 × 25/144

= 119/169 × 169/120 × 25/144

= 119 × 1/120 × 25/144

= 119 × 1/24 × 5/144

= 595/3456 [ ANS]

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