Question

If cos theta=(12)/(13) 0<theta<(pi)/(2) then (sin^(2)theta-cos^(2)theta)/(2sin theta cos theta)=
A) -(169)/(120)
B) (169)/(120)
C) -(119)/(120)
D) (119)/(120)​

Answer 1

Answer:

C. -$\frac{119}{120}$

Step-by-step explanation:

given cosα = 12/13

=> adj/hyp = 12/13

by pythogorean theorem,

opp = √(hyp²-adj²) = √(13²-12²) = √(169-144)

       = √25 = 5 units

=> sinα = opp/hyp = 5/13

∴ $\frac{sin^2\alpha-cos^2\alpha }{2. sin\alpha. cos\alpha }$  = $\frac{(\frac{5}{13} )^2-(\frac{12}{13} )^2}{2.\frac{5}{13}.\frac{12}{13} }$

                     = $\frac{\frac{25}{169}-\frac{144}{169} }{\frac{120}{169}}$  = -$\frac{144-25}{169} * \frac{169}{120}$

                     = -$\frac{119}{120}$