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Asked by Madhuri Last Modified
Answer To find the principal value of sin−1(−3−2)sin−1(−32)sin−1(−3−2)sin−1(−23), we'll start by finding the individual principal values of sin−1(−3−2)sin−1(−3−2
) and sin−1(−32)sin−1(−23), and then multiply them together.
Since sin−1sin−1 gives an angle whose sine is equal to the given value, we need to find an angle θθ such that sinθ=−3−2sinθ=−3−2
.
However, the sine function only returns values between -1 and 1. Therefore, −3−2−3−2
is outside the range of the sine function, and there is no real angle θθ for which sinθ=−3−2sinθ=−3−2. Hence, sin−1(−3−2)sin−1(−3−2
) is undefined.
Again, since sin−1sin−1 gives an angle whose sine is equal to the given value, we need to find an angle ϕϕ such that sinϕ=−32sinϕ=−23.
Similar to the previous case, −32−23 is outside the range of the sine function, and there is no real angle ϕϕ for which sinϕ=−32sinϕ=−23. Hence, sin−1(−32)sin−1(−23) is also undefined.
Therefore, the principal value of sin−1(−3−2)sin−1(−32)sin−1(−3−2
)sin−1(−23) is undefined.
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