What is the value of sec^2(arctan(2))-csc^2(arctan(3)) ?

The value of sec^2(arctan(2))-csc^2(arctan(3)) is 35/9

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sec^2(arctan(2))-csc^2(arctan(3))

sec^{2} (arctan (2)) - csc^{2} (arctan (3))

\frac{35}{9}

Solution steps

sec^{2} (arctan (2)) - csc^{2} (arctan (3))

Rewrite using trig identities:

csc (arctan (3)) = \frac{1 + 3 ^{2}}{3}

= sec^{2} (arctan (2)) - (\frac{1 + 3 ^{2}}{3})^{2}

Simplify

= sec^{2} (arctan (2)) - \frac{10}{9}

Rewrite using trig identities:

sec (arctan (2)) = 5

= (5)^{2} - \frac{10}{9}

Simplify

(5)^{2} - \frac{10}{9} : \frac{35}{9}

= \frac{35}{9}

50 \cdot sin (4 0^{\circ})

6 cos (16 0^{\circ}) + 4 cos (29 0^{\circ})

sin (- 90 0^{\circ})

arcsin (\frac{11}{16})

arcsin (\frac{11}{15})

What is the value of sec^2(arctan(2))-csc^2(arctan(3)) ?
The value of sec^2(arctan(2))-csc^2(arctan(3)) is 35/9