Math, asked by psynapse8581, 10 months ago

3cosΦ=2
2sec^2Φ+2tan^2Φ-7=?

Answers

Answered by ITzBrainlyGuy
1

Answer:

given

3 \cos( \theta)  = 2 \\  \cos( \theta)  =  \frac{3}{2}

 \sec( \theta)  =  \frac{2}{3}  \\

we know that

 \tan( \theta)  =  \sqrt{1 -  { \sec( \theta) }^{2} }

 \tan( \theta )  =  \sqrt{1 -  { (\frac{2}{3} )}^{2} }  \\  \tan( \theta)  =  \sqrt{ \frac{9 - 4}{9} }  \\  \tan(  \theta)  =  \sqrt{ \frac{5}{9} }  \\  \tan( \theta)  =  \frac{ \sqrt{5} }{3}

{\mathrm{\underline{\underline \pink {to  \:  \: find:}}}}

2 { \sec( \theta) }^{2}  + 2 { \tan( \theta) }^{2}  - 7

 = 2 {( \frac{2}{3}) }^{2}  + 2 {( \frac{ \sqrt{5} }{3} )}^{2} \\   \\  = 2( \frac{4}{9} ) + 2( \frac{5}{9}) \\   \\ =  \frac{8}{9}   +  \frac{10}{9}  \\   \\ =   \frac{18}{9}  \\  = 2

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