Question

If sin23 ° = p, then the value of sin67 ° is calculated as p

Answer 1

Answer:

root(1-p^2)

Step-by-step explanation:

sin67

=cos(90-67)

=cos23

=root(1-sin^23)

=root(1-p^2)

Answer 2

Answer:

sin67°=(1-p²)/p²

Step-by-step explanation:

sin 90°= 1

sin(A+B)=sinA×cosB+cosA×sinB

sin(23°+67°)=sin23°cos67°+cos23°sin67°=1

p×cos67°+cos23°sin67°=1

p×sin(90°-67°)+cos23°sin67°=1

p×sin23°+cos23°sin67°=1

p²+cos23°sin67°=1 .................(1)

sin23°=p

sin²23°=p²...........(squaring both side)

1-cos²23°=p²..........(sin²A=1-cos²A)

cos²23°=1-p²

cos23°=√(1-p²)

putting value of cos 23° in eq. 1

p²+√(1-p²)sin67°=1

√(1-p²)sin67°=1-p²

sin67°=(1-p²)/p²