Question

Hey friends solve it
Wrong answer will reported. ​

Answer 1

EXPLANATION.

⇒ [tan20°/cosec70°]² + [cot20°/sec70°]² + 2 tan75° tan45° tan 15°.

As we know that,

We can write equation as,

⇒ [tan20°/cosec(90° - 20°)]² + [cot20°/sec(90° - 20°)]² + 2 tan75° (1) tan (90° - 75°).

⇒ [tan20°/sec20°]² + [cot20°/cosec20°]² +2 tan75° cot 75°.

⇒ [sin20°/cos20°/1/cos20°]² + [cos20°/sin20°/1/sin20°] + 2 tan 75° X 1/tan 75°.

⇒ [sin²20°] + [cos²20°] + 2.

⇒ 1 + 2.

⇒ 3.

                                                                                             

MORE INFORMATION.

(1) = sin²∅ + cos²∅ = 1.

(2) = 1 + tan²∅ = sec²∅.

(3) = 1 + cot²∅ = cosec²∅.

(4) = sin2∅ = 2 sin∅ cos∅ = 2tan∅/1 + tan²∅.

(5) = cos2∅ = cos²∅ - sin²∅ = 2 cos²∅ - 1 = 1 - 2 sin²∅ = 1 - tan²∅/1 + tan²∅.

(6) = tan2∅ = 2tan∅/1 - tan²∅.

(7) = sin3∅ = 3 sin∅ - 4 sin³∅.

(8) = cos3∅ = 4 cos³∅ - 3 cos∅.

(9) = tan3∅ = 3 tan∅ - tan³∅/1 - 3 tan²∅.

Answer 2

★$\huge\bf{\blue{\underline{Question:-}}}$

• In the given attachment.

————————————————————————————

★$\huge\bf{\red{\underline{Answer:-}}}$

☯$\large\sf{\pink{3}}$

————————————————————————————

$\huge\bf{\green{\underline{Explanation:-}}}$

$\large\sf{[tan20°/cosec70°]²+[cot20°/sec70°]²+2tan75°tan45°tan15°}$.

★$\large\bf{\blue{\underline{Then,\: write \:the\: equation \:as\: :-}}}$

☯$\large\sf{[tan\:20°\:/\:cosec\:(90°\:-\:20°)]²+[cot\:20°/sec\:(90°\:-\:20°)]²+2\:tan\:75°\:(1)\:tan\:(90°\:-\:75°)}$

☯$\large\sf{[tan\:20°\:/\:sec\:20°]²+[cot\:20°\:/\:cosec\:20°]²+2\:tan\:75°\:cot\:75°}$

☯$\large\sf{[sin\:20°\:/\:cos\:20°\:/\:1\:/\:cos\:20°]²+[cot\:20°\:/\:sin\:20°\:/\:1\:/\:sin\:20°]²+2\:tan\:75°\:\times{\:1\:/\:tan\:75°}}$

☯$\large\sf{[sin²\:20°]+[cos²\:20°]\:+\:2}$

☯$\large\sf{1\:+\:2}$

☯$\large\sf{3}$

————————————————————————————