If sec tita + tan tita = p,then show that sin tita =p²-1 / p²+1.
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Answered by
8
LHS = p² - 1 / p² + 1
= (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
= RHS
lilly4189:
thank you ! :D
did u undrstnd..
yeah
in wich class r u???
Answered by
5
RHS= p2-1/p2+1
= (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
= (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
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