Question

If tan ( 20°–3 Θ) = cot(5 Θ –20°), then find the value of Θ and
hence evaluate
sin Θ secΘ tanΘ – cosec Θ cos Θ cot Θ ​

Answer 1

Answer:

Given, θ  is an acute angle and  tanθ=8/15.

In figure we have, 

tanθ=BC/AB=8/15

So, BC=8  and  AB=15    

By Pythagoras theorem, we have

AC=(AB2+BC2)=(52+82)

=(25+64)

=289

⇒AC=17.

Now,

secθ=AC/AB=17/15

cosecθ=AC/BC=17/8

So,

secθ+cosecθ=17/15+17/8

=(136+255)/120

=391/120

=313031.

Answer 2

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