Question

if sinA + cosA = root 2 sinA then value of tanA is if A is not equal to 90°​

Answer 1

Answer:

$tanA = \sqrt{2} + 1$

Step by step explanation:

$sinA+cosA= \sqrt{2} sinA \\ </p><p>cosA= \sqrt{2} sinA-sinA \\ </p><p>cosA=sinA( \sqrt{2} -1) \\ </p><p> \frac{cosA}{sinA} = \sqrt{2} -1 \\ </p><p> \frac{sinA}{cosA} = \frac{1}{ \sqrt{2} - 1 } \\ </p><p>tanA= \frac{1}{ \sqrt{2} - 1} \times \frac{ \sqrt{2} + 1}{ \sqrt{2 } + 1 } \\ tanA = \frac{ \sqrt{2} + 1 }{ {( \sqrt{2} )}^{2} - {(1)}^{2} } \\ tanA = \frac{ \sqrt{2} + 1 }{2 - 1} \\ tanA = \frac{ \sqrt{2} + 1 }{1} \\ tanA = \sqrt{2} + 1$