Question

solve : 2sinA-1=0
hence find : cos2A + tan2A​

Answer 1

Answer:

$\displaystyle{\boxed{\red{\sf\:\cos\:(\:2A\:)\:+\:\tan\:(\:2A\:)\:=\:\dfrac{3}{2}\:}}}$

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:2\:\sin\:A\:-\:1\:=\:0}$

We have to find the value of

$\displaystyle{\sf\:\cos\:(\:2A\:)\:+\:\tan\:(\:2A\:)}$

Now,

$\displaystyle{\sf\:2\:\sin\:A\:-\:1\:=\:0}$

$\displaystyle{\implies\sf\:2\:\sin\:A\:=\:1}$

$\displaystyle{\implies\:\boxed{\purple{\sf\:\sin\:A\:=\:\dfrac{1}{2}}}}$

Now, we know that,

$\displaystyle{\boxed{\pink{\sf\:\cos\:(\:2x\:)\:=\:1\:-\:2\:\sin^2\:(\:x\:)\:}}}$

$\displaystyle{\therefore\sf\:\cos\:(\:2A\:)\:=\:1\:-\:2\:\sin^2\:A}$

$\displaystyle{\implies\sf\:\cos\:(\:2A\:)\:=\:1\:-\:2\:(\:\sin\:A\:)^2}$

$\displaystyle{\implies\sf\:\cos\:(\:2A\:)\:=\:1\:-\:2\:\left(\:\dfrac{1}{2}\:\right)^2}$

$\displaystyle{\implies\sf\:\cos\:(\:2A\:)\:=\:1\:-\:\cancel{2}\:\times\:\dfrac{1}{\cancel{2}}\:\times\:\dfrac{1}{2}}$

$\displaystyle{\implies\sf\:\cos\:(\:2A\:)\:=\:1\:-\:\dfrac{1}{2}}$

$\displaystyle{\implies\sf\:\cos\:(\:2A\:)\:=\:\dfrac{2\:-\:1}{2}}$

$\displaystyle{\implies\:\boxed{\orange{\sf\:\cos\:(\:2A\:)\:=\:\dfrac{1}{2}}}}$

Now, we know that,

$\displaystyle{\boxed{\green{\sf\:\tan\:(\:x\:)\:=\:\dfrac{\sin\:(\:x\:)}{\cos\:(\:x\:)}\:}}}$

$\displaystyle{\therefore\:\sf\tan\:(\:2A\:)\:=\:\dfrac{\sin\:(\:2A\:)}{\cos\:(\:2A\:)}}$

$\displaystyle{\implies\sf\:\tan\:(\:2A\:)\:=\:\dfrac{\dfrac{1}{2}}{\dfrac{1}{2}}}$

$\displaystyle{\implies\sf\:\tan\:(\:2A\:)\:=\:\dfrac{1}{\cancel{2}}\:\times\:\cancel{2}}$

$\displaystyle{\implies\:\boxed{\pink{\sf\:\tan\:(\:2A\:)\:=\:1\:}}}$

Now, we have to find the value of

$\displaystyle{\sf\:\cos\:(\:2A\:)\:+\:\tan\:(\:2A\:)}$

$\displaystyle{\implies\sf\:\cos\:(\:2A\:)\:+\:\tan\:(\:2A\:)\:=\:\dfrac{1}{2}\:+\:1}$

$\displaystyle{\implies\sf\:\cos\:(\:2A\:)\:+\:\tan\:(\:2A\:)\:=\:\dfrac{1\:+\:2}{2}}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:\cos\:(\:2A\:)\:+\:\tan\:(\:2A\:)\:=\:\dfrac{3}{2}\:}}}}$

Answer 2

Answer:

answer is 3

2

Step-by-step explanation:

hope it helpful To u