Question

If sin θ + cos θ = 3 , then tan θ + cot θ = ?​

Answer 1

Step-by-step explanation:

Given.. sin@ + cos@= 3

Squaring on both the sides

Sin^2@ + cos^2@ + 2sin@cos@ = 9

As we know sin^2@ + cos^2@ = 1

1 + 2sin@cos@=9

2sin@cos@ =9-1

sin@cos@ = 8/2

Sin@cos@ = 4 ------- (1)

Now tan@ + cot@

= Sin@/cos@ + cos@/sin@

= sin^2@ + cos^2@ / cos@sin@

We know sin^2@ + cos^2@ = 1

So it will be,

= 1/cos@sin@

Now from (1)

=1/4

So tan@ + cot@ = 1/4