Math, asked by arpan572, 10 months ago

If {cos}^{ - 1} ( \frac{ - 1}{2} ) - {sin}^{ - 1}( \frac{1}{2} )

Answers

Answered by ashishyelonde3103
0

Step-by-step explanation:

lets \:  \cos (\frac{1}{2} ) =  \alpha  \\  \:  \:   \  \:  \:  \:  \:  \:  \: cos( \alpha )  =  \frac{1}{2}  \\ hence \: sin( \alpha ) =  \frac{ \sqrt{3} }{2}  \\ lets \:  \: sin( \frac{1}{2} ) =  \beta  \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:\sin( \beta )  =  \frac{1}{2}  \\ hence \:  \: cos( \beta ) =  \frac{ \sqrt{3} }{2}  \\  \cos(( \alpha   -  \beta )  =  \cos( \alpha ) \cos( \beta )    +  \sin( \alpha )  \sin( \beta )  \\ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  =   \frac{1}{2}  \times  \frac{ \sqrt{3} }{2}  +  \frac{ \sqrt{3} }{2}  \times  \frac{1}{2}  \\ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   =  \frac{ \sqrt{3} }{4}  +  \frac{ \sqrt{3} }{4}  \\  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   = 2 \frac{ \sqrt{3} }{4}  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: =  \frac{ \sqrt{3} }{2}

Answered by Anonymous
1

Answer:

this us the same question but another

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