Question

prove that , tan theta / tan (90°- theta) +sin(90°- theta)/cos theta = sec^2 theta​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

LHS:

tanϑ / tan(90-ϑ) + sin(90-ϑ)/cosϑ

= tanϑ/cotϑ + cosϑ/cosϑ

*Complementary angles*

= sinϑ/cosϑ ÷ cosϑ/sinϑ + 1

= sinϑ/cosϑ × sinϑ/cosϑ + 1

= sin²ϑ / cos²ϑ + 1

= (sin²ϑ+cos²ϑ) / cos²ϑ

*take LCM*

= 1/cos²ϑ

*Identity—sin²ϑ + cos²ϑ = 1*

= sec²ϑ

= RHS

LHS = RHS

Hence proved.

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