Question

the ticks are correct but please answer with proper explanation.​

Answer 1

Answer:

107) In the expression in the brackets, the numbers in the denominators cancel with the previous numerators, so

$\displaystyle\frac12\cdot\frac23\cdot\frac34\cdots\frac{x-1}{x-2} = x-1$

So the equation becomes

sin 2(x-1) = 1

=> 2(x-1) = 90°    [ since 0° < x < 100° ]

=> x-1 = 45°

=> x = 46°

108) cos θ + sin θ = √2 cos θ

=> sin θ = ( √2 - 1 ) cos θ      ... (1)             [ subtracted cos θ from both sides ]

=> -sin θ = ( 1 - √2 ) cos θ                        [ multiplied by -1 ]

=> cos θ - sin θ = ( 2 - √2 ) cos θ             [ added cos θ ]

=> cos θ - sin θ = √2 ( √2 - 1 ) cos θ        [ factor out √2 ]

=> cos θ - sin θ = √2 sin θ                      [ from equation (1) ]