Question

Sin theta+cos theta is equal to the a and sincube theta +cos cube theta is equal to the b then 3a-2b is equal to dash

Answer 1

Find the value of (3a-2b):

Step-by-step explanation:

$\ Given \ value:\\\\\sin \theta + \cos \theta = a\\\\\sin^3 \theta + \cos^3 \theta=b\\\\\ find:\\\\3a-2b= ?\\\\\ Solution:\\\\3a-2b\\\\3(\sin \theta + \cos \theta) - 2(\sin^3 \theta + \cos^3 \theta)\\\\\rightarrow 3(\sin \theta + \cos \theta) - 2(\sin^3 \theta + \cos^3 \theta)\\\\\ fromula:\\\\(\sin^3 \theta + \cos^3 \theta)= (\sin \theta + \cos \theta) (\sin^2 \theta + \cos^2 \theta-\sin \theta \cos \theta)$

$\rightarrow 3(\sin \theta + \cos \theta) - 2[(\sin \theta + \cos \theta) (\sin^2 \theta + \cos^2 \theta-\sin \theta \cos \theta)]\\\\\therefore \sin^2 \theta + \cos^2 \theta =1 \\\\ \rightarrow 3(\sin \theta + \cos \theta) - 2[(\sin \theta + \cos \theta) (1-\sin \theta \cos \theta)]\\\\\rightarrow 3(\sin \theta + \cos \theta) - 2(\sin \theta + \cos \theta)+2(\sin \theta + \cos \theta) (\sin \theta \cos \theta)]$

$\rightarrow (\sin \theta + \cos \theta) (1+2\sin \theta \cos \theta)\\\\\rightarrow (\sin \theta + \cos \theta) (\sin^2\theta+\cos^2\theta+2\sin \theta \cos \theta)\\\\\rightarrow (\sin \theta + \cos \theta) (\sin \theta + \cos \theta)^2\\\\\rightarrow (\sin \theta + \cos \theta)^3$

Learn more:

• Find the value: https://brainly.in/question/7833010