Question

SIMPLIFY(cosecQ+cotQ)(1-cosQ) ​

Answer 1

Answer:

Step-by-step explanation:

when you multiply them

cosecQ - cosecQ x cosQ + cotQ - cotQ x cosQ

(1-cosQ)(cosecQ+cotQ)

(1-cosQ)(1\sinQ+cosQ\sinQ)

1-cosQ×1+cosQ\sinQ

(1-cosQ)(1+cosQ)\sinQ

1-cos^2Q\sinQ

sin^2 theta + cos^2 theta = 1

1 - cos^2 theta = sin^2 theta

sin^2Q/sinQ

sinQ and sinQ  will get cancel

so answer is sinQ

Answer 2

ANSWER

$( \csc \alpha + \cot \alpha )(1 - \cos \alpha ) \\ \\ (\frac{1}{ \sin \alpha } + \frac{ \cos \alpha }{ \sin \alpha } )(1 - \cos \alpha ) \\ \\ ( \frac{1 + \cos \alpha }{ \sin \alpha } )(1 - \cos \alpha ) \\ \\ (1 - { \cos}^{2} \alpha ) \frac{1}{ \sin \alpha } \\ \\ \frac{ {sin}^{2} \alpha }{ \sin \alpha } = \sin \alpha$

FORMULA USED...

$\cot \alpha = \frac{ \cos \alpha }{ \sin \alpha } \\ \\ \csc \alpha = \frac{1}{ \sin \alpha } \\ \\ 1 - {cos}^{2} \alpha = {sin}^{2} \alpha \\ \\ ( 1 - cos \alpha )(1 + \cos \alpha ) = 1 - {cos}^{2} \alpha$

ANSWER BY...

PURPLE WORLD

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