Find the value of tan(135°) + cot(45°) using co-function identities.

A) 1

B) \$ (5√3)/3 \$

C) 0

D) - 1

A ladder leans against a vertical wall. The foot of the ladder is placed 6 meters away from the wall. When the ladder is leaning against the wall, the top of the ladder is 8 meters above the ground. What is the length of the ladder?

A) 56 meters

B) 48 meters

C) 27 meters

D) 10 meters

Prove the quotient identity: \$(cos^2 (θ))/(1 - sin(θ)) + (1 - sin(θ))/(cos^2 (θ)) = sec^2 (θ)\$.

A) \$LHS ne RHS\$

B) LHS = RHS

C) LHS = Infinity

D) None of the above

Prove the identity \$sec(θ) − cos(θ) = sin(θ)/sin(θ + π/2)\$.

A) proved

B) not proved

C) 0

D) None of the above

Simplify the expression:

\$ (sin(x) cos(90^\circ - x) + cos(x) sin(90^\circ - x))/(tan(x) + cot(x) )\$

A) \$ 1/(2csc(2x))\$

B) \$2csc(x)\$

C) \$ 2/(sec(3x))\$

D) \$ 2/(3cot(2x))\$

If \$ sin(x) = 24/25 \$​, find the values of cot(90°− x) and sec(90°− x).

A) \$ 7/24, 25/24 \$

B) \$ 24/7, 25/24 \$

C) \$ 24/7, 24/25 \$

D) \$ 7/24, 24/25 \$

Prove the quotient identity: \$ ( sin^2(θ) / (1−cos(θ)))​+ ((1−cos(θ)​)/ sin^2(θ)) = csc^2(θ) \$

A) Infinity

B) Proved

C) Zero

D) Not Proved

If \$ tan( pi/2 - x ) + cot( pi/2 ​− x ) = 5 \$, what is value of tanx?

A) \$ (5 ± \sqrt23) / 2 \$

B) \$ (5 ± \sqrt21) / 4 \$

C) \$ (5 ± \sqrt21) / 2 \$

D) \$ (4 ± \sqrt21) / 2 \$

Find the value of tan 150° + cot 30° using cofunction identities.

A) \$ (4\sqrt3)/3 \$

B) \$ (5\sqrt3)/3 \$

C) \$ (2\sqrt3)/3 \$

D) \$ (1\sqrt3)/3 \$

A person standing 10 meters away from the base of a building observes that the angle of elevation to the top of the building is 60°. At the same time, another person standing on the roof of the buliding observes that the angle of depression to the first person is 45°.Find the height of the buliding.

A) 11 meters

B) 12 meters

C) 15 meters

D) 10 meters