Prove tht sinA(sinA + sin 3A) is non-negative for all real values of A experts plz reply soon ....

awantika dubey

Prove tht sinA(sinA + sin 3A) is non-negative for all real values of Aexperts plz reply soon ..... rates assured.

taran

=

sin^2 A + 1/2(2sinAsin3A)

=

sin^2 A + 1/2[cos2A -cos4A]

= sin^2 A +1/2 [ cos2A - 2cos^2 2A + 1]

=

1/2 [ 2sin^2 A +cos2A - 2cos^2 2A + 1]

=

1/2 [ 1 -2cos^2 2A + 1]

=

1- cos^2 2A

=

sin^2 2A

which is non negative

Srujana

Simply expand it, you get

$sinA(sinA+3sinA-4sin^{3}A)$

$=4sin^2A(1-sin^{2}A)$

$=4sin^{2}Acos^{2}A$

which is always non negative

Arjun Virmani

Apply sin3A = 3sinA - 4sin³A

sinA + sin3A = sinA + 3sinA - 4sin³A = 4sinA - 4sin³A

so sinA(sinA+sin3A) = sinA(4sinA - 4sin³A)

= 4sin²A.(1-sin²A)

= 4sin²Acos²A

= sin²2A which is non-negative...... $$$$

ghfh bgd

Ask & Discuss Questions with Community & Experts