Question

2 log (cos teta)+log (1+tan² teta) =​

Answer 1

Given Expression,

2log(cos∅) + log(1 + tan²∅)

Using Power Rule,

$\longrightarrow$ log(cos ²∅)

Using product rule of logarithm,

$\longrightarrow$ log[cos²∅(1 + tan²∅)]

We know that,

sec²∅ - tan²∅ = 1 >> sec²∅ = 1 + tan²∅

Now,

$\longrightarrow$ log(cos²∅sec²∅)

$\longrightarrow$ log[cos²∅/cos²∅]

$\longrightarrow$ log(1)

$\longrightarrow$ 0

Answer 2

Given :-

2log(cos∅) + log(1 + tan²∅)

Using Power Rule,:-

⟶ log(cos ²∅)

Using product rule of logarithm,

⟶ log[cos²∅(1 + tan²∅)]

We know that,

sec²∅ - tan²∅ = 1 >> sec²∅ = 1 + tan²∅

Now,

⟶ log(cos²∅sec²∅)

⟶ log[cos²∅/cos²∅]

⟶ log(1)

⟶ 0