Question

if tanA+sinA=m and tanA-sinA=n then prove that m²-n²=4√mn​

Answer 1

Answer:

Step-by-step explanation:

tanA+sinA=m

=> m²=(tanA+sinA)²=tan²A+2tanAsinA+sin²A

tanA-sinA=n

=>n²=(tanA-sinA)²=tan²A-2tanAsinA+sin²A

Now,m²-n²=tan²A+2tanAsinA+sin²A-(tan²A-2tanAsinA+sin²A)

=4tanAsinA

Again,4√mn=4√(tan²A-sin²A)=4√sin²A(1/cos²A-1)=4√sin²A(sin²A/cos²A)= 4√(sin²Atan²A)=4tanAsinA

so,m²-n²=4√mn(proved)

Thanks You.Hope this solution helps you to understand.

Answer 2

Answer:

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