Question

tan²theta + cot²theta = 4/sin² 2theta -2​

Answer 1

Answer:

tan^2 theta + cot^2 theta = 4/sin^2 2theta -2

Step-by-step explanation:

tan^2 theta + cot^2 theta

= sin^2 theta /cos^2 theta + cos^2 theta /sin^2 theta

=( sin^4 theta + cos^4 theta )/(sin^2 theta × cos^2 theta )

={(sin^2 theta + cos^2 theta)^2 - 2×sin^2 theta ×cos^2 theta}/(sin^2 theta × cos^2 theta)

= (1 - 2×sin^2 theta × cos^2 theta )/(sin^2 theta×cos^2 theta)

= 1/(sin^2 theta × cos^2 theta) - 2

= 4/(4× sin^2 theta × cos^2 theta) - 2

= 4/(2×sin theta × cos theta)^2 -2

= 4/(sin 2theta)^2 -2

= 4/sin^2 2theta -2

Answer 2

ANSWER IS GIVEN BELOW

STEP BY STEP EXPLANATION IS ALSO GIVEN

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