Question

If tan A + sin A = m and tan A - sin A = n, prove that (m? - n2)2 = 16 mn.
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Answer 1

HEY MATE YOUR ANSWER IS HERE

★ CORRECT QUESTION ★

TAN A + SIN A = m AND

TAN A - SIN A = n

THEN PROVE THAT ( m² - n² )² = 16 mn

★ SOLUTION ★

ACCORDING TO QUES

(m² - n²) = ( m + n ) ( m - n )

now place the values of m & n

( m²-n² ) =

( TAN A + SIN A + TAN A - SIN A )( TAN A + SINA - TAN A + SIN A )

( m²-n²) = ( 2 TAN A ) ( 2 SIN A )

( m²-n²) = 4 TAN A . SIN A

hence ,

( m²-n²)² = 16 TAN²A . SIN²A -----------eq 1

now

m × n = ( TAN A + SIN A ) ( TAN A - SIN A )

m × n = TAN ² A - SIN² A

m × n = ( SIN² A / COS ² A ) - SIN² A

m × n = ( SIN² A - SIN²A COS² A)/ ( SIN² A)

AFTER TAKING SIN²A COMMON IN ABOVE EQ WE WILL FINALLY GET

m × n = TAN²A × SIN² A -----------eq 2

now ,

by equation 1 and 2

(m²-n²)² = 16 m. n

Thanks for the question hope this helps

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# RISHU HERE

Answer 2

Answer:

Hope it will be helpful to you all