Question

if tanA=1 and cosB=1 then find the value of sin (a+b)​

Answer 1

Step-by-step explanation:

tanA=1

tanA=tan45

A=45

cosB=1

cosB=cos0

B=0

so,sin(A+B)=sin(45+0)

sin45=1/√2

Answer 2

$\huge{\underline{\bf\red{QuestiØn} :}}$

$\sf If \: \tan A = 1 \: and \: \cos B, \\ \sf then \: find \: the \: value \: of \\ \sf \sin(A + B).$

$\huge{\underline{\bf\blue{SolutiØn}\ :}}$

We have,

$\begin{aligned} \\ \tan A& = 1 \\ \\ \implies \tan A& = \tan45 \degree \\ \\ \iff \quad \ \ A & = 45 \degree \ [ \because \tan 45 \degree = 1 ] \\ & \sf [on \: comparing \: both \: the \: sides] & & & & & & \end{aligned}$

And,

$\begin{aligned} \\ \cos B& = 1 \\ \\ \implies \cos B& = \cos0 \degree \\ \\ \iff \quad \ \ B & = 0 \degree \ [ \because \cos 0 \degree = 1 ] \\ & \sf [on \: comparing \: both \: the \: sides] & & & & & & \end{aligned}$

HENCE ,

$\begin{aligned} \\ \sin(A + B)& = \sin(45 \degree + 0 \degree) \\ \\ & = \sin45 \degree \\ \\ & = \boxed{\frac{1}{ \sqrt{2} }} \\ & & & & & & & \end{aligned}$

$\red{\rule{5.5cm}{0.02cm}}$

$\Large{ \mid {\underline{\underline{\bf\green{BrainLiest \ AnswEr}}}} \mid }$