Express cos 2 -isin 2 -5cos 3 -isin 3 -6sin-i cos-3 in the form of A - i B isA- cos 25 -i sin 25 -B- icos 25 -i sin 25 -C- icos 25 -i sin 25 -D- cos 25 -i sin 25 -

The correct option is C sinθ icosθ= i^2 sinθ icosθ = i(cosθ+isinθ) Given expression is nbsp; ( i)^3 [cos( 10θ 18θ+3θ+isin( 25θ)] =i(cos25θ ising 25 θ ] ...

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Standard XI

Mathematics

Euler's Representation

Express cos 2...

Question

Express $(c o s 2 θ + i s i n 2 θ)^{- 5}$ $(c o s 3 θ - i s i n 3 θ)^{6}$ $(s i n θ - i c o s θ)^{3}$ in the form of A+iB is

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Solution

The correct option is C

sin $θ$ -icos $θ$ = - $i^{2}$ sin $θ$ -icos $θ$ = -i(cos $θ$ +isin $θ$ )

Given expression is

$(- i)^{3}$ [cos(-10 $θ$ -18 $θ$ +3 $θ$ +isin(-25 $θ$ )]

=i(cos25 $θ$ - ising 25 $θ$ ] .

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Express (cos2θ+isin2θ)−5 (cos3θ−isin3θ)6 (sinθ−icosθ)3 in the form of A+iB is

The correct option is C sinθ-icosθ= -i2 sinθ-icosθ = -i(cosθ+isinθ) Given expression is (−i)3 [cos(-10θ-18θ+3θ+isin(-25θ)] =i(cos25θ - ising 25 θ ] .

Express $(c o s 2 θ + i s i n 2 θ)^{- 5}$ $(c o s 3 θ - i s i n 3 θ)^{6}$ $(s i n θ - i c o s θ)^{3}$ in the form of A+iB is

The correct option is C

sin $θ$ -icos $θ$ = - $i^{2}$ sin $θ$ -icos $θ$ = -i(cos $θ$ +isin $θ$ )

Given expression is

$(- i)^{3}$ [cos(-10 $θ$ -18 $θ$ +3 $θ$ +isin(-25 $θ$ )]

=i(cos25 $θ$ - ising 25 $θ$ ] .