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# trignometry challenge

GIVEN (a^2-b^2)sintheta +2abcostheta = a^2 +b^2

TO FIND = tantheta

i am not able to sole this problem need help...

Note by Avn Bha
2 years, 5 months ago

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how did u get it? · 2 years, 5 months ago

@avn bha , My answer is quite long. So please try to find any shorter way (if any) and do tell me... Dividing the given eqn. by $$cos{ \theta }$$. You get the equation in terms of $$\tan { \theta } \quad and\quad \sec { \theta }$$. Squaring both sides and converting $$\sec ^{ 2 }{ \theta } =1+\tan ^{ 2 }{ \theta }$$ and simplifying, u get an equation, quadratic in $$\tan { \theta }$$ which looks like

$$4{ a }^{ 2 }{ b }^{ 2 }\tan ^{ 2 }{ \theta } -4ab({ a }^{ 2 }-{ b }^{ 2 })\tan { \theta } +{ ({ a }^{ 2 }-{ b }^{ 2 }) }^{ 2 }=0\\ Using\quad quadratic\quad formula\quad you\quad get\quad \\ \tan { \theta } =\frac { 4ab({ a }^{ 2 }-{ b }^{ 2 }) }{ 8{ a }^{ 2 }{ b }^{ 2 } } =\frac { { a }^{ 2 }-{ b }^{ 2 } }{ 2ab }$$

CHEERS!!!:) · 2 years, 5 months ago

$$\tan \theta = \frac{a^{2}-b^{2}}{2ab}$$ · 2 years, 5 months ago