Use trigonometric expressions to build an equivalent trigono

Use trigonometric expressions to build an equivalent trigonometric identity with the given expression: sin (x) tan (x) sec (x) = ? cot^2 (x) csc^2 (x) tan^2 (x) sec^2 (x)

Solution

Solution:

sin(x) * tan(x) *sec(x) = ?

now tan(x) = sin(x) / cos(x)

sec (x) = 1 / cos(x)

plug this value into above

sin(x) * (sin(x)/cos(x) ) * 1/cos(x)

=(sin(x)* sin(x) )/ (cos(x) * cos(x))

= sin²(x) / cos²(x)

= (sin(x)/cos(x) )²

Now tan(x) = sin(x) / cos(x)

= (tan²(x) )

option (c) is correct

Answer