Question

Prove that

`4cot45 ^(2) - 3tan ^(2) 60 + 2sec ^(2)60 = 3`
help me​

Answer 1

`4 \cot {}^(2) (45) - 3 \tan {}^(2) (60) + 2 \sec {}^(2) (60) = 3 \\`

`LHS = 4 \cot {}^(2) (45) - 3 \tan {}^(2) (60) + 2 \sec {}^(2) (60) \\`

let us first take a look at the values of the trigonometric ratios given in the question so that we get quite clear about what is to be done.

here ,

`\cot(45) = 1 \\ \\ \tan(60) = √(3) \\ \\ \sec(60) = 2`

now ,

we just have to plug in the values considering certain other things given in the question and we're done!

so let's start ~

`4(1) {}^(2) - 3( √(3) ) {}^(2) + 2(2) {}^(2) \\ \\ \dashrightarrow \: 4(1) - 3(3) + 2(4) \\ \\ \dashrightarrow \: 4 - 9 + 8 \\\\ \dashrightarrow \: 12 - 9 \\ \\\dashrightarrow \: 3 = RHS`

hence , proved ~

hope helpful :D