how to solve cos70/sin20+cos57cosec33-2cos60?
Did you notice that in the first two terms the angles mentioned are complimentary angles?
And did you know that cos 70 = sin 20 ?
so....
cos70/sin20+cos57cosec33-2cos60
= cos70/sin20 + cos57/sin33 - 2cos60
= sin20/sin20 + cos57/cos57 - 2cos60
= 1+1 - 2(1/2)
= 1
To solve the expression cos70/sin20+cos57cosec33-2cos60, we can proceed step by step.
Step 1: Simplify the expression using trigonometric identities:
We know that csc(x) is equal to 1/sin(x) and sec(x) is equal to 1/cos(x).
So, we can rewrite the expression as:
cos70/sin20 + cos57 * (1/sin33) - 2cos60
Step 2: Simplify further.
Let's evaluate each part of the expression separately:
a) cos70/sin20:
- To evaluate cos70, we need to use a calculator or a table of trigonometric values.
- Similarly, to evaluate sin20, we also need to use a calculator or a table of trigonometric values.
- Divide cos70 by sin20.
b) cos57 * (1/sin33):
- Evaluate cos57 using a calculator or a table of trigonometric values.
- Multiply cos57 by (1/sin33).
c) 2cos60:
- Evaluate cos60 using a calculator or a table of trigonometric values.
- Multiply cos60 by 2.
Step 3: Combine the simplified expressions:
Add the values obtained from step 2a, 2b, and 2c together.
This process will give you the final solution for the given expression.