The value of $$sin8$$⁡θ$$+cos8$$⁡θ$$+sin6$$⁡θ$$cos2$$⁡θ $$+3sin4$$⁡θ$$cos2$$⁡θ$$+cos6$$⁡θ$$sin2$$⁡θ$$+3sin2$$⁡θ$$cos4$$⁡θ is equal to

Question

The value of $$sin8$$⁡θ$$+cos8$$⁡θ$$+sin6$$⁡θ$$cos2$$⁡θ $$+3sin4$$⁡θ$$cos2$$⁡θ$$+cos6$$⁡θ$$sin2$$⁡θ$$+3sin2$$⁡θ$$cos4$$⁡θ is equal to

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We have, $$sin8$$⁡θ$$+cos8$$⁡θ$$+sin6$$⁡θ$$cos2$$⁡θ$$+3sin4$$⁡θ$$cos2$$⁡θ$$+cos6$$⁡θ$$sin2$$⁡θ$$+3sin2$$⁡θ$$cos4$$⁡θ $$=sin8$$⁡θ$$+cos8$$⁡θ$$+sin2$$⁡θ$$cos2$$⁡θ(sin4$$⁡θ$$+cos4$$⁡θ$$+3sin2$$⁡θ$$+3cos2$$⁡θ$$) $$=(sin4$$⁡θ$$+cos4$$⁡θ$$)2$$−$$2sin4$$⁡θ$$cos4$$⁡θ$$+14sin2$$⁡$$2$$θ$${(sin2$$⁡θ$$+cos2$$⁡θ$$)2$$−$$12sin2$$⁡$$2$$θ$$+3}$$ $$=1$$−$$sin2$$⁡$$2$$θ$$42$$−$$18sin4$$⁡$$2$$θ$$+sin2$$⁡$$2$$θ−$$18sin4$$⁡$$2$$θ $$=1+12sin2$$⁡$$2$$θ−$$316sin4$$⁡$$2$$θ $$=116(16+8sin2$$⁡$$2$$θ−$$3sin4$$⁡$$2$$θ$$)$$

The value of $\sin^{8} θ + \cos^{8} θ + \sin^{6} {θcos}^{2} θ$ $+ 3 \sin^{4} {θcos}^{2} θ + \cos^{6} {θsin}^{2} θ + 3 \sin^{2} {θcos}^{4} θ$ is equal to

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The value of sin8⁡θ+cos8⁡θ+sin6⁡θcos2⁡θ +3sin4⁡θcos2⁡θ+cos6⁡θsin2⁡θ+3sin2⁡θcos4⁡θ is equal to

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The value of $\sin^{8} θ + \cos^{8} θ + \sin^{6} {θcos}^{2} θ$ $+ 3 \sin^{4} {θcos}^{2} θ + \cos^{6} {θsin}^{2} θ + 3 \sin^{2} {θcos}^{4} θ$ is equal to