If $$sin$$â¡Î¸$$+$$$$cos$$â¡Î¸$$=a$$ and $$cos$$â¡Î¸â$$sin$$â¡Î¸$$=b$$, $$sin$$â¡Î¸$$($$$$sin$$â¡Î¸â$$cos$$â¡Î¸$$)+sin2$$â¡Î¸$$sin2$$â¡Î¸â$$cos2$$â¡Î¸$$+sin3$$â¡Î¸$$sin3$$â¡Î¸â$$cos3$$â¡Î¸$$+$$â¦ is equal to

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If $$sin$$â¡Î¸$$+$$$$cos$$â¡Î¸$$=a$$ and $$cos$$â¡Î¸â$$sin$$â¡Î¸$$=b$$, $$sin$$â¡Î¸$$($$$$sin$$â¡Î¸â$$cos$$â¡Î¸$$)+sin2$$â¡Î¸$$sin2$$â¡Î¸â$$cos2$$â¡Î¸$$+sin3$$â¡Î¸$$sin3$$â¡Î¸â$$cos3$$â¡Î¸$$+$$â¦ is equal to

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We $$havesin2$$â¡Î¸$$+sin4$$â¡Î¸$$+sin6$$â¡Î¸$$+$$â¯.....â$$sin$$â¡Î¸$$cos$$â¡Î¸$$+sin2$$â¡Î¸$$cos2$$â¡Î¸$$+sin3$$â¡Î¸$$+cos3$$â¡Î¸$$+$$â¯ $$=sin2$$â¡Î¸$$1$$â$$sin2$$â¡Î¸â$$sin$$â¡Î¸$$cos$$â¡Î¸$$1$$â$$sin$$â¡Î¸$$cos$$â¡Î¸$$=1$$â$$cos$$â¡$$2$$Î¸$$1+$$$$cos$$â¡$$2$$Î¸â$$sin$$â¡$$2$$Î¸$$(2$$â$$sin$$â¡$$2$$Î¸$$)=1$$â$$ab1+ab+1$$â$$a23-a2$$

If $\sin â¡ Î¸ + \cos â¡ Î¸ = a$ and $\cos â¡ Î¸ â \sin â¡ Î¸ = b,$ $\sin â¡ Î¸ (\sin â¡ Î¸ â \cos â¡ Î¸) + \sin^{2} â¡ Î¸ (\sin^{2} â¡ Î¸ â \cos^{2} â¡ Î¸) +$ $\sin^{3} â¡ Î¸ (\sin^{3} â¡ Î¸ â \cos^{3} â¡ Î¸) + â¦$ is equal to

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If sinâ¡Î¸+cosâ¡Î¸=a and cosâ¡Î¸âsinâ¡Î¸=b, sinâ¡Î¸(sinâ¡Î¸âcosâ¡Î¸)+sin2â¡Î¸sin2â¡Î¸âcos2â¡Î¸+sin3â¡Î¸sin3â¡Î¸âcos3â¡Î¸+â¦ is equal to

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If $\sin â¡ Î¸ + \cos â¡ Î¸ = a$ and $\cos â¡ Î¸ â \sin â¡ Î¸ = b,$ $\sin â¡ Î¸ (\sin â¡ Î¸ â \cos â¡ Î¸) + \sin^{2} â¡ Î¸ (\sin^{2} â¡ Î¸ â \cos^{2} â¡ Î¸) +$ $\sin^{3} â¡ Î¸ (\sin^{3} â¡ Î¸ â \cos^{3} â¡ Î¸) + â¦$ is equal to