Question

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Answer 1

Answer:

$\huge\bf\blue{QuestioN}$

If cos teta = 3/5 then find sec²teta + tan²teta.

$\huge\bf\blue{AnsweR$

• cos teta = 3/5

• cos teta = adjacent/hypotenuse

• here , adjacent = 3k

• here , hypotenuse = 5k

• here , opposite = ?

By Pythagoras theorem ,

hypo² = adj² + opp²

(5k)² = (3k)² + opp²

25k² = 9k² + opp²

opp² = 25k² - 9k²

opp² = 16k²

opp = √16k²

opp = 4k

• sec teta = opposite/hypotenuse

• sec teta = 4k/5k

• sec teta = 4/5

• tan teta = opposite / adjacent

• tan teta = 4k/3k

• tan teta = 4/3

Now ,sec²teta + tan²teta. =

➡️ (4/5)² + (4/3)²

➡️ 16/25 + 16/9

➡️ 16 × 9/25×9 + 16×25/9×25

➡️ 144/225 + 400/225

➡️ 144+400/225

➡️ 544/225