Question

Find all the values of 'x' satisfying 0 <x< 180and
tan2x + cot2x= 2.​

Answer 1

Step-by-step explanation:

3

=∣sinxcosx∣+

2+tan

2

x+cot

2

x

⇒

3

=∣sinxcosx∣+

tan

2

x+cot

2

x+2tanxcotx

⇒

3

=∣sinxcosx∣+

(tanx+cotx)

2

⇒

3

=∣sinxcosx∣+∣(tanx+cotx)∣=∣sinxcosx∣+

∣

∣

∣

∣

∣

sinxcosx

sin

2

x+cos

2

x

∣

∣

∣

∣

∣

⇒

3

=∣sinxcosx∣+

∣sinxcosx∣

1

≥2 ...{∵AM≥GM}

∵

3

≥2 is not possible.

Therefore x have no solution.