2sin(x+45)=1 ?

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between 0<=x<=180

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Answer 1 · 2017-08-20T07:05:47

#x=105.#

We know that,

#sin(180-theta)=sintheta, and, sin(360+theta)=sintheta.#

Now, #2sin(x+45)=1 rArr sin(x+45)=1/2=sin30.#

#:. x+45=30, or, (180-30), or, (360+30), or, (540-30), ....,#

i.e., #x+45=30, or, 150, or, 390, or, 510, ...#

#:. x=30-45, or, 150-45, or, 390-45, or, 510-30, ....#

#:. x=-15, or, 105, or, 345, or, 480, ...#

Of these, only #x=105" satisfies the cond. "0lexle180.#