Question

The value of sin(450 + α) – cos (450 – α) is




Select one:
a. 2sinα
b. 0
c. 1
d. 2cosα​

Answer 1

Answer:

correct answer is A

Step-by-step explanation:

i am not sure

Answer 2

$\textbf{To find:}$

$\textsf{The value of}\;\mathsf{sin(450^\circ+\alpha)-cos(450^\circ-\alpha)}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\mathsf{sin(450^\circ+\alpha)-cos(450^\circ-\alpha)}$

$\mathsf{Using,}$

$\boxed{\mathsf{sin(A+B)=sinA\,cosB+cosA\,sinB}}$

$\boxed{\mathsf{cos(A-B)=cosA\,cosB+sinA\,sinB}}$

$\mathsf{=[sin450^\circ\,cos\alpha+cos450^\circ\,sin\alpha]-[cos450^\circ\,cos\alpha+sin450^\circ\,sin\alpha]}$

$\mathsf{=[sin(360^\circ+90^\circ)\,cos\alpha+cos(360^\circ+90^\circ)\,sin\alpha]-[cos(360^\circ+90^\circ)\,cos\alpha+sin(360^\circ+90^\circ)\,sin\alpha]}$

$\mathsf{=[sin90^\circ\,cos\alpha+cos90^\circ\,sin\alpha]-[cos90^\circ\,cos\alpha+sin90^\circ\,sin\alpha]}$

$\mathsf{=[(1)\,cos\alpha+(0)\,sin\alpha]-[(0)\,cos\alpha+(1)\,sin\alpha]}$

$\mathsf{=(cos\alpha+0)-(0+sin\alpha)}$

$\mathsf{=cos\alpha-sin\alpha}$

$\implies\boxed{\mathsf{sin(450^\circ+\alpha)-cos(450^\circ-\alpha)=cos\alpha-sin\alpha}}$