Question

cos (alfa+beta)=0
then sin (alfa+2beta)=?
​

Answer 1

Answer:

cot(α+β)=0

∴

sin(α+β)

cos(α+β)

=0 ∴ cos(α+β)=0

α+β=90

∙

∴ sin(α+β)=1 cos(α+β)=0

sin(α+2β)=sin(α+2β+α−α)

=sin[(2α+2β)−α]

=sin[2(α+β)−α]

=sin2(α+β)cosα−cos2(α+β)sinα

=2sin(α+β)cos(α+β)cosα−[cos

2

(α+β)−sin

2

(α+β)]sinα

=2×1×0×cosα−[0−1]sinα

=0+sinα

=sinα

Step-by-step explanation:

please mark me brain list

Answer 2

★Question★

$\bf \: If \: cos( \alpha + \beta ) = 0 \: then \: sin( \alpha + 2 \beta ) =$

★Answer★

★Given :-

$\bf \:cos( \alpha + \beta ) = 0$

★To find :-

$\bf \:sin( \alpha + 2 \beta )$

★Solution:-

$\bf \:cos( \alpha + \beta ) = 0$

$\bf\implies \:\bf \:\alpha + \beta = 90°$

$\bf \:So, \: sin( \alpha + 2 \beta )$

$\bf\implies \:\:sin( \alpha + \beta + \beta )$

$\bf\implies \:sin(90° + \beta )$

$\bf\implies \: cos \beta$

_____________________________________________