Question

If tan theta + cot theta= 2. find the value of tan sq theta + cot sq theta
​

Answer 1

Given :-

TanΦ + CotΦ = 2

Answer :-

TanΦ + Cot Φ = 2

Squaring both side,

( TanΦ + Cot Φ ) ^2 = 2^2

By using identity ( a + b) ^2

= a^2 + b^2 + 2ab

Tan^2Φ + Cot^2 Φ + 2 * tanΦ * Cot Φ = 4

As we know that, TanΦ * CotΦ = 1

Tan^2Φ + Cot^2Φ + 2 = 4

Tan^2Φ + Cot^2Φ = 4 - 2

Tan^2Φ + Cot^2Φ = 2

Some more info :-

• Tan Φ = Sin Φ / Cos Φ

• Cot Φ = Cos Φ / Sin Φ

• Sec Φ = 1 / Cos Φ

• Cosec Φ = 1 / Sin Φ

Answer 2

Answer:

Valueof

tan

2

θ+cot

2

θ=2

Step-by-step explanation:

Given \: tan\theta+cot\theta=2\:---(1)Giventanθ+cotθ=2−−−(1)

/* On Squaring both sides of the equation, we get

\left(tan\theta+cot\theta\right)^{2}=2^{2}(tanθ+cotθ)

2

=2

2

\implies tan^{2}\theta+cot^{2}\theta+2 tan\theta cot\theta = 4⟹tan

2

θ+cot

2

θ+2tanθcotθ=4

\implies tan^{2}\theta+cot^{2}\theta+2 \times 1 = 4⟹tan

2

θ+cot

2

θ+2×1=4

/* tanAcotA = 1 */

\implies tan^{2}\theta+cot^{2}\theta = 4-2⟹tan

2

θ+cot

2

θ=4−2

\implies tan^{2}\theta+cot^{2}\theta = 2⟹tan

2

θ+cot

2

θ=2

Therefore,

tan^{2}\theta+cot^{2}\theta = 2tan

2

θ+cot

2

θ=2