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## Answers

__= (sec θ + tanθ)² - 1 / (sec θ + tanθ)² + 1__

__= sec²θ + tan²θ + 2 secθ tanθ - 1 / sec²θ + tan²θ + 2 secθ tanθ + 1__

__= (sec²θ 1) + tan² θ + 2 secθ tanθ / (tan² θ + 1) + sec² θ + 2 secθ tanθ__

= tan² θ + tan² θ + 2 secθ tanθ / sec²θ + sec²θ + 2 secθ tanθ

__= 2 tan²θ + 2 secθ tanθ / 2 sec² θ + 2 secθ tanθ__

= 2 tanθ (tanθ + secθ) / 2 secθ (tanθ + secθ)

__= tanθ / secθ__

= (sinθ/ cosθ) / (1/cosθ)

= sinθ

= RHS

= (sec θ + tanθ)² - 1 / (sec θ + tanθ)² + 1

__= sec²θ + tan²θ + 2 secθ tanθ - 1 / sec²θ + tan²θ + 2 secθ tanθ + 1__

__= (sec²θ 1) + tan² θ + 2 secθ tanθ / (tan² θ + 1) + sec² θ + 2 secθ tanθ__

= tan² θ + tan² θ + 2 secθ tanθ / sec²θ + sec²θ + 2 secθ tanθ

__= 2 tan²θ + 2 secθ tanθ / 2 sec² θ + 2 secθ tanθ__

= 2 tanθ (tanθ + secθ) / 2 secθ (tanθ + secθ)

__= tanθ / secθ__

= (sinθ/ cosθ) / (1/cosθ)

= sinθ