What is csc(1+tan^2(θ)) ?

The solution to csc(1+tan^2(θ)) is csc(sec^2(θ))

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simplify csc(1+tan^2(θ))

simplify

csc (1 + tan^{2} (θ))

csc (sec^{2} (θ))

Solution steps

csc (1 + tan^{2} (θ))

Rewrite using trig identities

= csc (1 + \frac{sin ^{2} ( θ )}{cos ^{2} ( θ )})

Rewrite using trig identities

= csc (1 + tan^{2} (θ))

Use the Pythagorean identity:

tan^{2} (x) + 1 = sec^{2} (x)

= csc (sec^{2} (θ))

sin (27 0^{\circ} - θ)

2 sin (x - 3 0^{\circ}) + cos (x)

sec (x - \frac{π}{4})

cos (- a)

sin (tan^{(- 1)} (x))