If the combined value of A and B is \$π/2\$, find the value of \$(1 - "sin"^2("A")) (1 - "cos"^2("A")) times (1 + "cot"^2("B")) (1 + "tan"^2("B"))\$.

The given expression

\$(1 - "sin"^2("A")) (1 - "cos"^2("A")) times (1 + "cot"^2("B")) (1 + "tan"^2("B"))\$

Combine value A and B is 90° so here A + B = 90° then A = 90° - B.

\$(1 + "tan"^2("B")) = "sec"^2("B") \$ and \$1 + "cot"^2("B") = "cosec"^2("B")\$.

So here plug the formulas in the given expression

\$(1 - "sin"^2("A")) (1 - "cos"^2("A")) times "cosec"^2("B") times "sec"^2("B")\$

\$"sin"^2("A") = "sin"^2(90 - "B") = "cos"^2"B" \$ and \$"cos"^2"A" = "cos"^2(90 - "B") = "sin"^2"B"\$

So now plug the hint in the above expression

\$(1 - "cos"^2("B")) (1 - "sin"^2("B")) times "cosec"^2("B") times "sec"^2("B"))\$

\$(1 - "cos"^2("B") = "sin"^2("B")) and (1 - "sin"^2("B") = "cos"^2("B"))\$

Now substitute these formulas into the expression

\$"sin"^2("B") "cos"^2("B") times 1/ ("cos"^2("B")) times 1/ ("sin"^2("B")) = 1\$

So, the value of the given expression is 1.

The expression involves squares of trigonometric functions, and squaring doesn’t always result in 2

2

The simplified expression should be in a positive value, not a negative value

-1

The expression simplifies to 1, rather than the previously stated -2, which was incorrect

-2

This is correct due to correct calculation by using the formula

1

Option

D

Can you summarize what you’ve understood in the above steps?