Maths-
General
Easy
Question
If
=
, then which of following statement is true -
.
=
and(
)n =![open square brackets table row cell cos to the power of n end exponent invisible function application alpha end cell cell sin to the power of n end exponent invisible function application alpha end cell row cell negative sin to the power of n end exponent invisible function application alpha end cell cell cos to the power of n end exponent invisible function application alpha end cell end table close square brackets](data:image/png;base64,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)
=
and(
)n =
.
=
and(
)n =
.
=
and(
)n =
The correct answer is:
.
=
and(
)n =![open square brackets table row cell cos invisible function application n alpha end cell cell sin invisible function application n alpha end cell row cell negative sin invisible function application n alpha end cell cell cos invisible function application n alpha end cell end table close square brackets](data:image/png;base64,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)
we are given matrix A and we are asked to find which of the given statements are true.
By using the properties of a matrix we verify that
.
=
and(
)n =![open square brackets table row cell cos invisible function application n alpha end cell cell sin invisible function application n alpha end cell row cell negative sin invisible function application n alpha end cell cell cos invisible function application n alpha end cell end table close square brackets](data:image/png;base64,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)
Therefore the correct option is choice 4
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