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Grade 12th passTrigonometry

If, tanA+sinA=m, tanA-sinA=n. Then prove that, tanA.sinA=√mn

Mahmudul Hasan

7 Years agoGrade 12th pass

1 Answer

Samyak Jain

7 Years ago

tanA + sinA = m …..(1) & tanA – sinA = n ….(2)

Simply multiply (1) & (2).

(tanA + sinA)(tanA – sinA) = mn

tan²A – sin²A = mn $\Rightarrow$ sin²A / cos²A – sin²A = mn

sin²A (1 – cos²A)/cos²A = mn

i.e. (sin²A/cos²A)(sin²A) = mn [1 – sin²A = cos²A]

tan²A . sin²A = $\sqrt{mn}$

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