Correct Answer - Option 4 : tan θ
Concept:
cos (90 + θ) = -sin θ
sin (180 + θ) = -sin θ
cot (90 - θ) = tan θ
sec (360 - θ) = sec θ
sec (270 - θ) = -cosec θ
Calculation:
\(\rm \frac{\cos (90+\theta)\sec (360-\theta) \tan (180-\theta )}{\sec (270-\theta )\sin (180+\theta )\cot (90-\theta )}\)
\(=\rm \frac{-\sinθ \secθ \ (-\tanθ )}{(-cosec\;θ )\ (-\sinθ )\tan θ }\)
\(=\rm \frac{\sinθ \secθ \ (\tanθ )}{(cosec\;θ )( \sinθ )\tan θ }\)
\(\rm = \frac{\sinθ}{\cosθ}\)
= tan θ
Hence, option (4) is correct.
