Find the value of cot θ.tan(90 - θ) - sec (90 - θ) cosec θ + (sin2 25° + sin2 65° ) + \(\sqrt {3 }\)(tan 30° tan 35° tan 55°).
Answer & explanation
Correct answer: option 1
cot θ.tan (90 - θ) - sec (90 - θ). cosec θ + (sin2 25° + sin2 65°)
+ \(\sqrt {3 }\) ( tan 35° tan 30° tan 55°)
= cot θ.cot θ - cosec θ. cosec θ + (sin2 25° + cos2 25°)
+ \(\sqrt {3 }\)(tan 30° tan 35° cot 35°)
= cot2 θ - cosec2 θ + (1) + \(\sqrt {3 }\)\(\frac{1}{\sqrt {3 }}\)
= -1 + 1 + 1 = 1 ( because sin2 θ + cos2 θ = 1 ⇒ tan θ cot θ = 1 × cot2 θ - cosec2 θ = 1)