Answer the following: Show that tan2θ + cot2θ ≥ 2 for all θ ∈ R - Mathematics and Statistics

Sum

Show that tan2θ + cot2θ ≥ 2 for all θ ∈ R

Solution

tan2θ + cot2θ  = tan^2theta + 1/tan^2theta

= (tan theta)^2 + (1/tantheta)^2

= (tan theta - 1/tan theta)^2 + 2tantheta* 1/tan theta  ...[∵ a2 + b2 = (a – b)2 + 2ab]

= (tan theta - 1/tan theta)^2 + 2 ≥ 2 for all θ ∈ R.

Concept: Signs of Trigonometric Functions in Different Quadrants
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 2 Trigonometry - 1
Miscellaneous Exercise 2 | Q 7 | Page 33