Question

if sin(50-3/2 α) = cos (3α-50), then find the value of α and hence evaluate;
tanα.secα.sinα-cotα.sinα.cosα.

Answer 1

sin(50-3α/2) = cos(3α-50)
sin(50-3α/2) = sin(90-3α+50)
sin(50-3α/2) = sin(140-3α)
50-3α/2 = 140-3α
3α/2 = 140-50 = 90
3α = 180
α = 60
Now,
          tanα.secα.sinα-cotα.sinα.cosα
=        sin²α/cos²α-cos²α
=         tan²α-cos²α = tan²60 - cos²60
=         (√3)² - (1/2)² = 3-1/4 = 11/4