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I made a circle in attachment …. .here theta = cos -1 x ...Lekin usne fir bhi theta ki value nhi rakhi ….wo theta ki value rakh ke bhi to x ke respect differential kar sakta tha …..please help me ….....

I made a circle in attachment ….            .here theta    = cos-1 x ...Lekin usne fir bhi theta ki value nhi rakhi ….wo theta ki value rakh ke bhi to x ke respect differential kar sakta tha …..please help me ….....

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Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Hello student,
Please find answer to your question
Yes, you can do by both ways.
The one which is done in the question is easy & less confusing.
You can do by directly putting the value of theta & use trigonometric identity
y = sin^{2}(\frac{\pi }{2}-\frac{\theta }{2})
sin(\frac{\pi }{2} - \alpha ) = cos\alpha
y = cos^{2}(\frac{\theta }{2})
cos(\alpha ) = 2 cos^{2}\frac{\alpha }{2}-1
y = \frac{1+cos\theta }{2}
y = \frac{1+coscos^{-1}x }{2}
y = \frac{1+x }{2}
\frac{dy}{dx} = \frac{1}{2}

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