Question

sec50÷sin40+cos40÷cosec50​

Answer 1

Answer:

2

Step-by-step explanation:

First, we should observe that the sum of angles in each of the product terms here is 90°. So, we should use complementary angle formula to simplify the expression.

We know that

sin(90°−θ)=cosθ

And

cos(90°−θ)=sinθ

Now,

sin40°=sin(90°−50°)=cos50°

Similarly,

cos40°=cos(90°−50°)=sin50°

Substitute these values in the given expression,

sec50°cos50°+sin50°cosec50°

=1cos50°.cos50°+sin50°.1sin50°

[∵secθ=1cosθ and cosecθ=1sinθ]

=1+1

=2