Question

Cosec(75°+theta)-sec(15-theta)-tan(55+theta)+cos(35-theta)

Answer 1

cosec (75° + θ) – sec (15° – θ) – tan (55° + θ) + cot (35° – θ)]

= [sec(90° - 75° - θ) - sec (15° – θ) – tan (55° + θ) + tan (90° - 35° + θ)]

= [sec (15° – θ) – sec (15° – θ) – tan (55° + θ) + tan (55° + θ)]

= 0

Answer: (B) 0

cos(α + β) = 0 => α + β = π/2 => α = π/2 - β

=> sin(α - β) = sin(π/2 - 2β) = cos2β

Answer : (B) cos2β

Let cos9α = sinα = k

=> sin9α = √(1-k^2) and cosα = √(1-k^2)

and cos10α = cos9α cosα - sin9α sinα = k√(1-k^2) - k√(1-k^2) = 0

=> 10α = π/2

=> 5α = π/4

=> tan(5α) = 1