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Seema Gopal
Asked: 2022-11-01T23:41:47+05:30 In:

If `x^n=a^m cos^4 theta ` and `y^n = b^m sin^4 theta` then `(i) (x^(n/2))/(a^(m/2))+ (y^(n/2))/(b^(m/2))=1` `(ii) x^n/a^m+y^n/b^m=1`(iii) `(x^(n/2))/(y^(n/2))+ (a^(m/2))/(y^(m/2))=1` (iv) None of these
A. `(x^(n//2))/(a^(m//2))+(y^(n//2))/(b^(m//2))=1`
B. `(x^(n))/(a^(m))+(y^(n))/(b^(m))=1`
C. `(x^(n//2))/(y^(n//2))+(a^(m//2))/(b^(m//2))=1`
D. None of these

If `x^n=a^m cos^4 theta ` and `y^n = b^m sin^4 theta` then `(i) (x^(n/2))/(a^(m/2))+ (y^(n/2))/(b^(m/2))=1` `(ii) x^n/a^m+y^n/b^m=1`(iii) `(x^(n/2))/(y^(n/2))+ (a^(m/2))/(y^(m/2))=1` (iv) None of these
A. `(x^(n//2))/(a^(m//2))+(y^(n//2))/(b^(m//2))=1`
B. `(x^(n))/(a^(m))+(y^(n))/(b^(m))=1`
C. `(x^(n//2))/(y^(n//2))+(a^(m//2))/(b^(m//2))=1`
D. None of these
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  1. Correct Answer – A
    `x^(n)=a^(m)cos^(4)theta, and y^(n)=b^(m)sin^(4)theta`
    `implies cos^(4)theta=(x^(n))/(a^(m)) and sin^(4) theta =(y^(n))/(b^(m))`
    `implies cos^(2) theta=(x^(n//2))/(a^(m//2)), sin^(4) theta=(y^(n//2))/(b^(m//2))`
    But, `sin^(2)theta+cos^(2)theta=1`
    `:. (x^(n//2))/(a^(m//2))+(y^(n//2))/(b^(m//2))=1`

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